This analysis was prepared by Francisco Arrieta and Jonathan Edwards.

1 Setup

# options(scipen=999) #prevent scientific notation
# options(scipen=-999) #encourage scientific notation
options(scipen=0) #encourage scientific notation neutral?
# kable table layout options
# do not display NAs and only 2 digits
opts <- options(knitr.kable.NA = '') #knitr.table.format = "latex"

# define table styling options
stable <- function(data, digits = 2) {
  knitr::kable(data, digits=digits) |> 
    # kable_styling(c("striped", "condensed"))
    kable_paper(full_width = F)
}

1.1 libraries

# modelling
library(psych) #factor analysis tools (PAF PAF)
library(lavaan) #causal analysis
library(lm.beta) # add standarized regression coeffs

# stats
library(nortest) #Kolmogorov-Smirnov-Test
library(corrplot) #correlation matrix plot
library(olsrr)  #VIF and Tolerance Values
library(pastecs) # provides function stat.desc
library(REdaS) #Bartelett's Test

# plotting & formatting
library(ggplot2) #better graphs
library(patchwork) # provides wrap_plots for multiplotting 
# library(gridExtra) #provides multiplotting functionality
# library(ggpubr) #provides ggarrange for multiplotting (patchwork better though)
library(semPlot) #for visualization of path diagrams (SEM)
library(lavaanPlot) #for visualization of path diagrams (SEM)
# library(rcompanion)   #Histogram and Normal Curve
library(kableExtra) #makes nice tables

# generic
library(dplyr) #useful data manip functions like arrange, distinct, rename etc included in fpp3
library(stringr) # provides string manip functions like str_split_fixed 
library(Hmisc) #describe function that describes features of dataframes
library(data.table) # creating and manipulating datatables
library(knitr) #rmarkdown tools not sure why useful
library(parameters) #get model outputs in table form (good for making tabs)

1.2 Load data

survey <- read.csv("Case Study III_Structural Equation Modeling.csv")
labels <- read.csv("Variables and Labels_Galeries Lafayette.csv")

dim(survey)
## [1] 553  45
# head(labels)

1.3 labels

#Make labels more readable
#create copy of label column without variable code
labels["Category"] <- sub("[^-]*\\s-","",labels[["Label"]]) 
# labels["Category"] <- sub(".*\\s-","",labels[["Label"]])
# labels

#split this new column (category) into category and short label
labels[c("Category","Label_short")] <- str_split_fixed(labels[["Category"]],"\\?\\s\\s|\\s-", n=2)
# labels[20:25,c("Category","Label_short")]
labels[,c("Variable","Category","Label_short")] |>
  stable()
Variable Category Label_short
Im1 What do GLB represent from your point of view Large Assortment
Im2 What do GLB represent from your point of view Assortment Variety
Im3 What do GLB represent from your point of view Artistic Decoration of Sales Area
Im4 What do GLB represent from your point of view Creative Decoration of Sales Area
Im5 What do GLB represent from your point of view Appealing Arrangement of Shop Windows
Im6 What do GLB represent from your point of view France
Im7 What do GLB represent from your point of view French Savoir-vivre
Im8 What do GLB represent from your point of view Expertise in French Traditional Cuisine
Im9 What do GLB represent from your point of view French Fashion
Im10 What do GLB represent from your point of view Gourmet Food
Im11 What do GLB represent from your point of view High-quality Cosmetics
Im12 What do GLB represent from your point of view Luxury brands
Im13 What do GLB represent from your point of view Up tp date Designer Brands
Im14 What do GLB represent from your point of view Gourmet specialities
Im15 What do GLB represent from your point of view Professional Selection of Brands
Im16 What do GLB represent from your point of view Professional Appearance Towards Customers
Im17 What do GLB represent from your point of view Are Trendy
Im18 What do GLB represent from your point of view Are Hip
Im19 What do GLB represent from your point of view Professional Organization
Im20 What do GLB represent from your point of view Relaxing Shopping
Im21 What do GLB represent from your point of view A Great Place to Stroll
Im22 What do GLB represent from your point of view Intimate Shop Atmosphere
C_CR1 CO-CREATION I would like to participate in an expert-workshop to improve the assortment of Galeries Lafayette Berlin.
C_CR2 CO-CREATION I would be available to take part in another survey at Galeries Lafayette Berlin.
C_CR3 CO-CREATION I would like to become a member of a customer group whose opinion is obtained for new products and major changes.
C_CR4 CO-CREATION I would like to participate in planning and designing special events (e.g. fashion show, introduction of new car models) if asked.
C_REP1 REPURCHASE I will continue to be a loyal customer of Galeries Lafayette Berlin.
C_REP2 REPURCHASE I intend to shop at Galeries Lafayette Berlin in the future.
C_REP3 REPURCAHSE I will surely visit Galeries Lafayette Berlin in the future.
COM_A1 AFFECTIVE COMMITMENT How strongly are you attached to Galeries Lafayette Berlin?
COM_A2 AFFECTIVE COMMITMENT How strongly are you emotionally connected to Galeries Lafayette Berlin?
COM_A3 AFFECTIVE COMMITMENT As a customer I feel (close) attached to GL
COM_A4 AFFECTIVE COMMITMENT feel a strong emotional bond toward GLB
SAT_1 SATISFACTION I am very satisfied with Galeries Lafayette Berlin.
SAT_2 SATISFACTION Overall, I am very satisfied with Galeries Lafayette Berlin.
SAT_3 SATISFACTION How satisfied are you with Galeries Lafayette Berlin?
SAT_P1 SATISFACTION EMPLOYEES The employees are capable and professional.
SAT_P2 SATISFACTION EMPLOYEES The employees know best about their products.
SAT_P3 SATISFACTION EMPLOYEES The employees are well-informed.
SAT_P4 SATISFACTION EMPLOYEES The employees are always helpful.
SAT_P5 SATISFACTION EMPLOYEES The employees are willing to respond to my questions in detail.
SAT_P6 SATISFACTION EMPLOYEES The employees are friendly.
TRU_1 TRUST I have the feeling that I can completely rely on GL.
TRU_2 TRUST GLB will always be honest and trustful with me.
TRU_3 TRUST GL will treat me always fair as a customer

1.4 Clean and handle missing data

# # omit all unanswered
# filter_all(survey, all_vars(. != 999))
# filter_all(survey, any_vars(. %in% c(999)))
# 
# filter_all(select(survey,1:22,"SAT_1"), all_vars(. != 999))
# filter_all(select(survey,1:22,"SAT_1"), any_vars(. %in% c(999)))
# 
# filter_all(data_img_EFA, all_vars(. != 999))
# filter_all(ges, any_vars(. %in% c(999)))
# delete variables unused in analysis (see case study instructions): 
survey <- survey |> select(-c("C_CR2", "SAT_P1", "SAT_P2", "SAT_P3", "SAT_P4", "SAT_P5", "SAT_P6", "TRU_1", "TRU_2", "TRU_3"))

# replace missing data (999) with NA
survey <- data.frame(sapply(survey,function(x) ifelse((x==999),NA,as.numeric(x))))

1.5 Explore Data

2 Dimensions by which Galeries Lafayette is perceived

2.1 ROUND 1: Exploratory factor analysis

2.1.1 Variable selection for EFA

# excluded image variables (in the first round of EFA we don't exclude any image variables...)
exclude=c() 

# the full survey data (includes dependent and independent variables) with excluded image variables (in this first round of EFA we don't exclude anything)
survey_excl_img <- survey |> select(-exclude)

# the data we will use for EFA (images)
data_img_EFA <- survey_excl_img[1:(22-length(exclude))]

2.1.2 handle missing data

# delete missing data (delete listwise)
data_img_EFA <- na.omit(data_img_EFA)

dim(survey)
## [1] 553  35
dim(survey_excl_img)
## [1] 553  35
dim(data_img_EFA)
## [1] 385  22

2.1.3 Check adequacy of correlation Matrix

2.1.3.1 correlation matrix

#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA)
corrplot(as.matrix(corr_matrix), 
         method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
         order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
         addCoef.col = 'black', number.cex = .5,
         tl.col ="black", 
         tl.cex = 0.80, 
         )

Variables to look out for going forward:

  • Images 9 and 11 are alone

  • Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).

2.1.3.2 Bartlett’s Test

bart_spher(data_img_EFA)
##  Bartlett's Test of Sphericity
## 
## Call: bart_spher(x = data_img_EFA)
## 
##      X2 = 6451.238
##      df = 231
## p-value < 2.22e-16

The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.

In our case we see that it is indeed rejected and that the data is not uncorrelated.

2.1.3.3 KMO

KMOTEST=KMOS(data_img_EFA)
print(KMOTEST, sort=T)
## 
## Kaiser-Meyer-Olkin Statistics
## 
## Call: KMOS(x = data_img_EFA)
## 
## Measures of Sampling Adequacy (MSA):
##       Im2       Im6       Im1      Im20      Im14      Im10       Im7       Im4 
## 0.8224640 0.8224827 0.8244624 0.8266391 0.8267452 0.8285789 0.8448231 0.8542604 
##      Im18       Im3      Im17      Im13      Im12      Im22      Im16      Im11 
## 0.8550678 0.8640362 0.8644991 0.8722220 0.8789413 0.8793157 0.9092200 0.9113882 
##      Im21       Im8       Im9      Im19       Im5      Im15 
## 0.9149654 0.9300079 0.9380091 0.9400714 0.9546668 0.9647563 
## 
## KMO-Criterion: 0.8770975

The KMO of 0.8770975 is above 0.6 which indicates the data is well suited for factor anlysis.

2.1.3.4 Anti-image Correlation

MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))

# Sort table
MSA_list<- MSA_list |> 
  setorder(cols = "MSA")

# Display table
MSA_list |> 
  stable() |>
  row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")
Item MSA
Im2 0.82
Im6 0.82
Im1 0.82
Im20 0.83
Im14 0.83
Im10 0.83
Im7 0.84
Im4 0.85
Im18 0.86
Im3 0.86
Im17 0.86
Im13 0.87
Im12 0.88
Im22 0.88
Im16 0.91
Im11 0.91
Im21 0.91
Im8 0.93
Im9 0.94
Im19 0.94
Im5 0.95
Im15 0.96

Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.

All variables have MSA above 0.5

2.1.4 Select method: PAF

2.1.4.1 Extract factors

EFA_PAF0 <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified
2.1.4.1.1 Scree plot
#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
     ylab="Eigenvalue",
     main="Scree plot",
     cex.lab=1.2,
     cex.axis=1.2,
     cex.main=1.8,
     col = "#0099F8",
     pch = 19) 
abline(h=1, col = "#7F35B2")

2.1.4.1.2 Kaiser Criterion
EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb
## [1] 6

The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.

There are 6 factors satisfying this condition.

2.1.4.1.3 Total Variance Explained
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
                                            seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
                                          EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
                                          Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
                                          Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |> 
  stable()
Factor number EigenValue Variance Total_Variance
1 8.98 40.81 0.41
2 2.47 11.21 0.52
3 1.56 7.10 0.59
4 1.46 6.62 0.66
5 1.25 5.67 0.71
6 1.15 5.22 0.77
7 0.81 3.68 0.80
8 0.71 3.23 0.84
9 0.57 2.58 0.86
10 0.46 2.08 0.88
11 0.36 1.64 0.90
12 0.33 1.51 0.91
13 0.29 1.34 0.93
14 0.28 1.29 0.94
15 0.25 1.13 0.95
16 0.23 1.04 0.96
17 0.20 0.92 0.97
18 0.19 0.85 0.98
19 0.16 0.72 0.99
20 0.12 0.53 0.99
21 0.10 0.46 1.00
22 0.08 0.37 1.00

With 6 factors we would explain 76.6310791% of total variance.

With 7 factors we would explain 80.3133487% of total variance.

# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue
## [1] 8.377985

2.1.4.2 Determine number of factors to retain

# select nb of factors to test
nf = c(5,6,7,8)

2.1.4.3 PAF orthogonal Varimax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()

i=1
for (n in nf) {
  # EFA_PAFn[[i]] <- n
  EFA_PAFn[[i]] <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn) <- nf
2.1.4.3.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
    EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn[[i]]$communality))

    # Sort table
    EFA_PAFn_communalities <- EFA_PAFn_communalities |>
      setorder(cols = "Communality")
    
    # Display table
    kbl <- EFA_PAFn_communalities |> 
              stable() |>
              row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn[[i]]$loadings["Im9",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im9 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im9 0.41
Im11 0.41
Im18 0.43
Im16 0.46
Im6 0.50
Im19 0.53
Im17 0.54
Im5 0.55
Im15 0.63
Im21 0.65
Im14 0.66
Im10 0.66
Im7 0.69
Im20 0.69
Im12 0.71
Im13 0.72
Im2 0.76
Im8 0.76
Im22 0.81
Im1 0.82
Im3 0.86
Im4 0.92

[1] “Communality for Im9 =0.405600881872799”

Number of factors = 6
Item Communality
Im11 0.45
Im9 0.46
Im16 0.47
Im19 0.52
Im5 0.55
Im18 0.57
Im15 0.63
Im21 0.65
Im17 0.70
Im13 0.70
Im6 0.71
Im12 0.73
Im8 0.74
Im14 0.76
Im2 0.76
Im10 0.78
Im7 0.78
Im20 0.79
Im22 0.79
Im1 0.84
Im3 0.85
Im4 0.92

[1] “Communality for Im9 =0.463399199002637”

Number of factors = 7
Item Communality
Im11 0.44
Im9 0.46
Im16 0.47
Im19 0.53
Im5 0.54
Im15 0.63
Im21 0.65
Im13 0.70
Im18 0.71
Im8 0.72
Im6 0.76
Im2 0.78
Im22 0.79
Im20 0.79
Im14 0.81
Im12 0.83
Im7 0.85
Im1 0.86
Im3 0.86
Im10 0.89
Im17 0.95
Im4 0.97

[1] “Communality for Im9 =0.455673655610471”

Number of factors = 8
Item Communality
Im11 0.45
Im9 0.46
Im5 0.58
Im19 0.62
Im15 0.65
Im21 0.65
Im13 0.70
Im8 0.72
Im18 0.74
Im6 0.76
Im22 0.78
Im16 0.80
Im2 0.81
Im20 0.81
Im12 0.84
Im7 0.85
Im14 0.85
Im3 0.86
Im10 0.90
Im17 0.93
Im1 0.94
Im4 0.97

[1] “Communality for Im9 =0.455554069181416”

Typically we should think about excluding variables with communalities below 0.3.

Based on the above, no variable should be excluded.

2.1.4.3.2 Factor loadings
# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}
Number of factors = 5
Variable MR2 MR5 MR4 MR1 MR3 Complexity Uniqueness
Im1 0.85 1.31 0.18
Im2 0.83 1.23 0.24
Im3 0.83 1.55 0.14
Im4 0.87 1.46 0.08
Im5 0.64 1.78 0.45
Im6 0.67 1.22 0.50
Im7 0.79 1.20 0.31
Im8 0.84 1.16 0.24
Im9 0.43 0.39 2.76 0.59
Im10 0.75 1.37 0.34
Im11 0.57 1.56 0.59
Im12 0.79 1.27 0.29
Im13 0.77 1.43 0.28
Im14 0.75 1.37 0.34
Im15 0.60 0.33 2.66 0.37
Im16 0.48 0.37 2.77 0.54
Im17 0.38 0.48 3.44 0.46
Im18 0.31 0.43 3.42 0.57
Im19 0.47 0.40 3.37 0.47
Im20 0.78 1.27 0.31
Im21 0.74 1.41 0.35
Im22 0.81 1.51 0.19
Number of factors = 6
Variable MR2 MR5 MR1 MR4 MR3 MR6 Complexity Uniqueness
Im1 0.86 1.30 0.16
Im2 0.83 1.24 0.24
Im3 0.83 1.51 0.15
Im4 0.88 1.42 0.08
Im5 0.64 1.74 0.45
Im6 0.61 0.56 2.12 0.29
Im7 0.72 0.48 1.88 0.22
Im8 0.81 1.25 0.26
Im9 0.35 0.32 0.43 3.51 0.54
Im10 0.80 1.42 0.22
Im11 0.59 1.62 0.55
Im12 0.79 1.34 0.27
Im13 0.73 1.66 0.30
Im14 0.80 1.42 0.24
Im15 0.60 2.76 0.37
Im16 0.48 0.37 2.78 0.53
Im17 0.35 0.31 0.39 0.54 3.66 0.30
Im18 0.35 0.50 3.48 0.43
Im19 0.46 0.40 3.45 0.48
Im20 0.84 1.22 0.21
Im21 0.73 1.43 0.35
Im22 0.79 1.60 0.21
Number of factors = 7
Variable MR5 MR1 MR3 MR2 MR4 MR7 MR6 Complexity Uniqueness
Im1 0.86 1.33 0.14
Im2 0.83 1.27 0.22
Im3 0.83 1.56 0.14
Im4 0.90 1.40 0.03
Im5 0.63 1.85 0.46
Im6 0.83 1.25 0.24
Im7 0.32 0.84 1.44 0.15
Im8 0.63 0.51 2.31 0.28
Im9 0.33 0.45 3.45 0.54
Im10 0.87 1.35 0.11
Im11 0.58 1.72 0.56
Im12 0.85 1.30 0.17
Im13 0.72 1.81 0.30
Im14 0.81 1.50 0.19
Im15 0.59 2.97 0.37
Im16 0.46 0.34 3.44 0.53
Im17 0.84 1.76 0.05
Im18 0.72 1.85 0.29
Im19 0.43 0.37 4.25 0.47
Im20 0.85 1.21 0.21
Im21 0.73 1.44 0.35
Im22 0.78 1.62 0.21
Number of factors = 8
Variable MR1 MR3 MR4 MR7 MR2 MR5 MR6 MR8 Complexity Uniqueness
Im1 0.88 1.45 0.06
Im2 0.82 1.45 0.19
Im3 0.81 1.66 0.14
Im4 0.89 1.47 0.03
Im5 0.65 1.84 0.42
Im6 0.83 1.23 0.24
Im7 0.84 0.30 1.40 0.15
Im8 0.54 0.59 2.56 0.28
Im9 0.33 0.46 3.34 0.54
Im10 0.87 1.41 0.10
Im11 0.58 1.72 0.55
Im12 0.86 1.28 0.16
Im13 0.72 1.78 0.30
Im14 0.83 1.49 0.15
Im15 0.47 0.39 4.81 0.35
Im16 0.77 1.78 0.20
Im17 0.82 1.82 0.07
Im18 0.74 1.76 0.26
Im19 0.30 0.54 3.68 0.38
Im20 0.86 1.20 0.19
Im21 0.73 1.44 0.35
Im22 0.78 1.63 0.22

Factor loadings:

  • Number of items per factor >=3
    • this condition is respected in all cases except when we have 8 factors. We eliminate the 8 factor solution
  • 0.40–0.30–0.20 rule: satisfactory variables (a) load onto their primary factor above 0.40, (b) load onto alter-native factors below 0.30, and (c) demonstrate a difference of 0.20 between their primary and alternative factor loadings.
    • 5 factor solution:
      • this condition is not respected for many variables. We eliminate the 5 factor solution
    • 6 factor solution:
      • this condition is not respected for: Im6, Im7, Im9, (Im11), (Im15), Im16, Im17, Im18, Im19 where Im17 and Im18 are particularly spread out
    • 7 factor solution:
      • this condition is not respected for: Im7, Im8, Im9, Im15, Im16, Im19 where Im16 and Im19 are particularly spread out

Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables.

Looking at the correlation matrix, we saw that variables Im16 and Im19 were highly correlated, we probably only need to exclude one of the two, Im19 has the lower communality of the two so we might consider eliminating that one.

Similarly Im17 and Im18 are highly correlated we might want to eliminate Im18 which has the lowest communality of the two, but they have adequately high loadings in the 7 factor solution so not a priority.

We might also exclude Im9 and Im15 as their communality is on the lower end and their loadings are spread out and quite weak. Also Im9 is problematic in both the 6 and 7 factor solution

Thurstone simple structure criteria:

  • Each row (variable) of the factor pattern matrix should have at least one zero

  • Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors

  • For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other

  • When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns

  • For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns

2.1.4.4 PAF oblique Promax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()

i=1
for (n in nf) {
  # EFA_PAFn_obl[[i]] <- n
  EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA, rotate="promax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn_obl) <- nf

length(EFA_PAFn_obl)
## [1] 4
2.1.4.4.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
    EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))

    # Sort table
    EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
      setorder(cols = "Communality")
    
    # Display table  
    kbl <- EFA_PAFn_obl_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn_obl[[i]]$loadings["Im9",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im9 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im9 0.41
Im11 0.41
Im18 0.43
Im16 0.46
Im6 0.50
Im19 0.53
Im17 0.54
Im5 0.55
Im15 0.63
Im21 0.65
Im14 0.66
Im10 0.66
Im7 0.69
Im20 0.69
Im12 0.71
Im13 0.72
Im2 0.76
Im8 0.76
Im22 0.81
Im1 0.82
Im3 0.86
Im4 0.92

[1] “Communality for Im9 =0.272947652560888”

Number of factors = 6
Item Communality
Im11 0.45
Im9 0.46
Im16 0.47
Im19 0.52
Im5 0.55
Im18 0.57
Im15 0.63
Im21 0.65
Im17 0.70
Im13 0.70
Im6 0.71
Im12 0.73
Im8 0.74
Im14 0.76
Im2 0.76
Im10 0.78
Im7 0.78
Im20 0.79
Im22 0.79
Im1 0.84
Im3 0.85
Im4 0.92

[1] “Communality for Im9 =0.339338697735652”

Number of factors = 7
Item Communality
Im11 0.44
Im9 0.46
Im16 0.47
Im19 0.53
Im5 0.54
Im15 0.63
Im21 0.65
Im13 0.70
Im18 0.71
Im8 0.72
Im6 0.76
Im2 0.78
Im22 0.79
Im20 0.79
Im14 0.81
Im12 0.83
Im7 0.85
Im1 0.86
Im3 0.86
Im10 0.89
Im17 0.95
Im4 0.97

[1] “Communality for Im9 =0.279736181915467”

Number of factors = 8
Item Communality
Im11 0.45
Im9 0.46
Im5 0.58
Im19 0.62
Im15 0.65
Im21 0.65
Im13 0.70
Im8 0.72
Im18 0.74
Im6 0.76
Im22 0.78
Im16 0.80
Im2 0.81
Im20 0.81
Im12 0.84
Im7 0.85
Im14 0.85
Im3 0.86
Im10 0.90
Im17 0.93
Im1 0.94
Im4 0.97

[1] “Communality for Im9 =0.302814913694533”

2.1.4.4.2 Factor loadings
# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}
Number of factors = 5
Variable MR2 MR5 MR1 MR4 MR3 Complexity Uniqueness
Im1 1.07 1.06 0.18
Im2 1.07 1.07 0.24
Im3 1.00 1.03 0.14
Im4 1.07 1.03 0.08
Im5 0.75 1.03 0.45
Im6 0.73 1.11 0.50
Im7 0.87 1.14 0.31
Im8 0.91 1.01 0.24
Im9 0.36 0.37 2.10 0.59
Im10 0.77 1.17 0.34
Im11 0.69 1.08 0.59
Im12 1.00 1.05 0.29
Im13 0.94 1.03 0.28
Im14 0.77 1.12 0.34
Im15 0.62 1.14 0.37
Im16 0.47 1.79 0.54
Im17 0.42 2.05 0.46
Im18 0.39 1.93 0.57
Im19 0.41 2.02 0.47
Im20 0.86 1.04 0.31
Im21 0.79 1.09 0.35
Im22 0.85 1.02 0.19
Number of factors = 6
Variable MR2 MR5 MR1 MR4 MR3 MR6 Complexity Uniqueness
Im1 1.05 1.06 0.16
Im2 1.03 1.07 0.24
Im3 0.99 1.03 0.15
Im4 1.06 1.05 0.08
Im5 0.74 1.03 0.45
Im6 0.52 0.68 2.22 0.29
Im7 0.65 0.56 2.24 0.22
Im8 0.80 1.05 0.26
Im9 0.48 1.95 0.54
Im10 0.81 1.23 0.22
Im11 0.67 1.15 0.55
Im12 0.91 1.03 0.27
Im13 0.79 1.09 0.30
Im14 0.80 1.18 0.24
Im15 0.60 1.18 0.37
Im16 0.46 1.81 0.53
Im17 0.57 1.97 0.30
Im18 0.54 1.91 0.43
Im19 0.39 2.15 0.48
Im20 0.92 1.07 0.21
Im21 0.76 1.07 0.35
Im22 0.80 1.04 0.21
Number of factors = 7
Variable MR5 MR1 MR2 MR3 MR4 MR7 MR6 Complexity Uniqueness
Im1 1.08 1.06 0.14
Im2 1.05 1.06 0.22
Im3 1.00 1.02 0.14
Im4 1.13 1.04 0.03
Im5 0.72 1.02 0.46
Im6 0.92 1.06 0.24
Im7 0.89 1.06 0.15
Im8 0.62 0.38 1.74 0.28
Im9 0.42 2.10 0.54
Im10 1.04 1.03 0.11
Im11 0.65 1.14 0.56
Im12 1.01 1.04 0.17
Im13 0.78 1.08 0.30
Im14 0.94 1.01 0.19
Im15 0.60 1.17 0.37
Im16 0.40 2.69 0.53
Im17 1.09 1.02 0.05
Im18 0.92 1.02 0.29
Im19 0.33 3.23 0.47
Im20 0.94 1.05 0.21
Im21 0.78 1.06 0.35
Im22 0.81 1.05 0.21
Number of factors = 8
Variable MR1 MR3 MR7 MR2 MR4 MR5 MR6 MR8 Complexity Uniqueness
Im1 1.04 1.01 0.06
Im2 0.95 1.02 0.19
Im3 0.90 1.02 0.14
Im4 1.03 1.03 0.03
Im5 0.72 1.11 0.42
Im6 0.98 1.06 0.24
Im7 0.95 1.05 0.15
Im8 0.43 0.49 2.39 0.28
Im9 0.45 1.92 0.54
Im10 0.97 1.01 0.10
Im11 0.66 1.15 0.55
Im12 1.04 1.05 0.16
Im13 0.79 1.06 0.30
Im14 0.92 1.02 0.15
Im15 0.35 0.36 2.73 0.35
Im16 1.02 1.03 0.20
Im17 0.98 1.01 0.07
Im18 0.90 1.01 0.26
Im19 0.63 1.11 0.38
Im20 0.98 1.09 0.19
Im21 0.79 1.06 0.35
Im22 0.82 1.06 0.22

7 factors: exclude 9, 15, 16, 19 6 factors: exclude 16, 17, 18, 19, 5 factors: exclude 17, 18

2.2 ROUND 2 : Exploratory factor analysis round 2

2.2.1 Variable selection for EFA

# # perform multiple variable selections
# 
# exclude <- list(c("Im1","Im2","Im16", "Im19","Im15","Im9"),
#              c("Im3","Im4","Im9", "Im15","Im11"))
# 
# survey_excl_img2 = list()
# data_img_EFA2 = list()
# 
# for (i in 1:length(exclude)){
#   survey_excl_img2[[i]] <- survey |> select(-exclude[[i]])
#   data_img_EFA2[[i]] <- survey_excl_img2[[i]][1:(22-length(exclude[[i]]))]
#   # print(survey_excl_img2[[i]])
# }
# 
# # survey_excl_img2[[1]]
# # survey_excl_img2[[2]]
# data_img_EFA2[[1]]
# data_img_EFA2[[2]]
# excluded image variables
# candidates for 7 factors: "Im9",("Im11"),"Im15", "Im19", "Im16"
# candidates for 6 factors: "Im16","Im9", "Im19", ("Im11"), ("Im15"), ("Im18"),"Im17", "Im6"

exclude=c("Im9","Im15","Im8") # "Im16", "Im19","Im9","Im11","Im15"

# the full survey data (includes dependent and independent variables) with excluded image variables
survey_excl_img2 <- survey |> select(-exclude) 

# the data we will use for EFA (images)
data_img_EFA2 <- survey_excl_img2[1:(22-length(exclude))]

The excluded variables correspond to the following:

excludedvars <- filter(labels, Variable %in% exclude)[c("Variable","Label_short")] 

excludedvars |>
  stable()
Variable Label_short
Im8 Expertise in French Traditional Cuisine
Im9 French Fashion
Im15 Professional Selection of Brands

2.2.2 handle missing data

# delete missing data
data_img_EFA2 <- na.omit(data_img_EFA2)

dim(survey)
## [1] 553  35
dim(survey_excl_img2)
## [1] 553  32
dim(data_img_EFA2)
## [1] 394  19

2.2.3 Check adequacy of correlation Matrix

2.2.3.1 correlation matrix

#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA2)
corrplot(as.matrix(corr_matrix), 
         method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
         order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
         addCoef.col = 'black', number.cex = .5,
         tl.col ="black", 
         tl.cex = 0.80,
         )

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Variables to look out for going forward: - Images 9 and 11 are alone - Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).

2.2.3.2 Bartlett’s Test

bart_spher(data_img_EFA2)
##  Bartlett's Test of Sphericity
## 
## Call: bart_spher(x = data_img_EFA2)
## 
##      X2 = 5521.451
##      df = 171
## p-value < 2.22e-16

The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.

In our case we see that it is indeed rejected and that the data is not uncorrelated.

2.2.3.3 KMO

KMOTEST=KMOS(data_img_EFA2)
print(KMOTEST, sort=T)
## 
## Kaiser-Meyer-Olkin Statistics
## 
## Call: KMOS(x = data_img_EFA2)
## 
## Measures of Sampling Adequacy (MSA):
##       Im6      Im10       Im7      Im14       Im2       Im1      Im20      Im18 
## 0.7471329 0.7642565 0.7744268 0.7843674 0.7950011 0.7961197 0.8143469 0.8323628 
##       Im4      Im17      Im12       Im3      Im13      Im22      Im11      Im16 
## 0.8394241 0.8427407 0.8483413 0.8497470 0.8567410 0.8730869 0.8958364 0.9007282 
##      Im21      Im19       Im5 
## 0.9102753 0.9199391 0.9515411 
## 
## KMO-Criterion: 0.8416876

The KMO of 0.8416876 is above 0.6 which indicates the data is well suited for factor anlysis.

2.2.3.4 Anti-image Correlation

MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))

#Display table
MSA_list<- MSA_list |> 
  setorder(cols = "MSA")
  
MSA_list |> 
  stable() |> 
  row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")
Item MSA
Im6 0.75
Im10 0.76
Im7 0.77
Im14 0.78
Im2 0.80
Im1 0.80
Im20 0.81
Im18 0.83
Im4 0.84
Im17 0.84
Im12 0.85
Im3 0.85
Im13 0.86
Im22 0.87
Im11 0.90
Im16 0.90
Im21 0.91
Im19 0.92
Im5 0.95

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.

All variables have MSA above 0.5

2.2.4 Select method: PAF

2.2.4.1 Extract factors

EFA_PAF0 <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified
2.2.4.1.1 Scree plot
#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
     ylab="Eigenvalue",
     main="Scree plot",
     cex.lab=1.2,
     cex.axis=1.2,
     cex.main=1.8,
     col = "#0099F8",
     pch = 19) 
abline(h=1, col = "#7F35B2")

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

2.2.4.1.2 Kaiser Criterion
EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb
## [1] 6

The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.

There are 6 factors satisfying this condition.

2.2.4.1.3 Total Variance Explained
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA2) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA2))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
                                            seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
                                          EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
                                          Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
                                          Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |> 
  stable()
Factor number EigenValue Variance Total_Variance
1 7.71 40.57 0.41
2 2.01 10.58 0.51
3 1.54 8.10 0.59
4 1.44 7.58 0.67
5 1.20 6.30 0.73
6 1.06 5.56 0.79
7 0.80 4.21 0.83
8 0.68 3.60 0.87
9 0.50 2.65 0.89
10 0.34 1.81 0.91
11 0.32 1.67 0.93
12 0.30 1.58 0.94
13 0.23 1.20 0.95
14 0.21 1.10 0.97
15 0.19 1.02 0.98
16 0.16 0.84 0.98
17 0.12 0.62 0.99
18 0.11 0.57 1.00
19 0.08 0.43 1.00

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

With 6 factors we would explain 78.6947762% of total variance.

With 7 factors we would explain 82.9058259% of total variance.

# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue
## [1] 7.109148

2.2.4.2 Determine number of factors to retain

# select nb of factors to test
nf = c(5,6,7,8)

2.2.4.3 PAF orthogonal Varimax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()

i=1
for (n in nf) {
  # EFA_PAFn[[i]] <- n
  EFA_PAFn[[i]] <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn) <- nf
2.2.4.3.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")

    EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn[[i]]$communality))

    # Sort table
    EFA_PAFn_communalities <- EFA_PAFn_communalities |>
      setorder(cols = "Communality")
    
    # Display table
    kbl <- EFA_PAFn_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn[[i]]$loadings["Im6",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im6 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im11 0.41
Im18 0.42
Im16 0.42
Im6 0.50
Im19 0.51
Im17 0.52
Im5 0.55
Im21 0.64
Im10 0.66
Im7 0.67
Im14 0.70
Im20 0.72
Im13 0.72
Im12 0.75
Im2 0.78
Im22 0.80
Im1 0.84
Im3 0.86
Im4 0.92

[1] “Communality for Im6 =0.496673139129337”

Number of factors = 6
Item Communality
Im16 0.42
Im11 0.45
Im19 0.51
Im5 0.55
Im6 0.64
Im21 0.64
Im18 0.65
Im13 0.69
Im10 0.71
Im7 0.73
Im12 0.74
Im14 0.74
Im20 0.78
Im22 0.79
Im2 0.80
Im17 0.83
Im3 0.86
Im1 0.89
Im4 0.92

[1] “Communality for Im6 =0.638799740882147”

Number of factors = 7
Item Communality
Im16 0.43
Im11 0.43
Im19 0.51
Im5 0.55
Im21 0.64
Im18 0.67
Im13 0.69
Im7 0.72
Im14 0.78
Im22 0.78
Im20 0.79
Im2 0.81
Im3 0.86
Im12 0.87
Im1 0.91
Im6 0.93
Im4 0.97
Im10 0.97
Im17 1.00

[1] “Communality for Im6 =0.931925021212407”

Number of factors = 8
Item Communality
Im11 0.43
Im5 0.58
Im21 0.64
Im16 0.67
Im18 0.68
Im13 0.69
Im7 0.69
Im19 0.70
Im2 0.76
Im14 0.78
Im22 0.78
Im20 0.81
Im3 0.86
Im12 0.87
Im4 0.97
Im6 0.99
Im10 1.00
Im17 1.00
Im1 1.00

[1] “Communality for Im6 =0.990898460352201”

Typically we should think about excluding variables with communalities below 0.3.

Based on the above, no variable should be excluded.

2.2.4.3.2 Factor loadings
# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
           
cat("\n\n")
}
Number of factors = 5
Variable MR1 MR2 MR4 MR5 MR3 Complexity Uniqueness
Im1 0.85 1.35 0.16
Im2 0.83 1.27 0.22
Im3 0.84 1.44 0.14
Im4 0.89 1.36 0.08
Im5 0.65 1.66 0.45
Im6 0.67 1.23 0.50
Im7 0.78 1.20 0.33
Im10 0.74 1.42 0.34
Im11 0.58 1.49 0.59
Im12 0.82 1.22 0.25
Im13 0.77 1.44 0.28
Im14 0.77 1.39 0.30
Im16 0.40 0.41 3.03 0.58
Im17 0.30 0.43 0.39 3.76 0.48
Im18 0.39 0.32 3.81 0.58
Im19 0.42 0.43 3.53 0.49
Im20 0.80 1.23 0.28
Im21 0.74 1.39 0.36
Im22 0.81 1.49 0.20
Number of factors = 6
Variable MR1 MR2 MR3 MR4 MR5 MR6 Complexity Uniqueness
Im1 0.86 1.40 0.11
Im2 0.83 1.33 0.20
Im3 0.85 1.43 0.14
Im4 0.89 1.35 0.08
Im5 0.65 1.63 0.45
Im6 0.73 1.40 0.36
Im7 0.81 1.24 0.27
Im10 0.70 0.32 1.95 0.29
Im11 0.61 1.46 0.55
Im12 0.80 1.31 0.26
Im13 0.71 1.80 0.31
Im14 0.73 0.32 1.85 0.26
Im16 0.41 0.39 3.16 0.58
Im17 0.74 2.15 0.17
Im18 0.66 2.10 0.35
Im19 0.43 0.39 3.93 0.49
Im20 0.84 1.21 0.22
Im21 0.73 1.43 0.36
Im22 0.79 1.54 0.21
Number of factors = 7
Variable MR1 MR3 MR4 MR5 MR2 MR6 MR7 Complexity Uniqueness
Im1 0.87 1.40 0.09
Im2 0.83 1.35 0.19
Im3 0.84 1.46 0.14
Im4 0.92 1.33 0.03
Im5 0.64 1.73 0.45
Im6 0.93 1.17 0.07
Im7 0.33 0.75 1.62 0.28
Im10 0.92 1.32 0.03
Im11 0.57 1.70 0.57
Im12 0.88 1.23 0.13
Im13 0.72 1.76 0.31
Im14 0.77 0.30 1.67 0.22
Im16 0.38 0.37 3.99 0.57
Im17 0.88 1.60 0.00
Im18 0.70 1.84 0.33
Im19 0.40 0.37 4.52 0.49
Im20 0.85 1.19 0.21
Im21 0.73 1.43 0.36
Im22 0.79 1.55 0.22
Number of factors = 8
Variable MR1 MR3 MR4 MR5 MR2 MR7 MR6 MR8 Complexity Uniqueness
Im1 0.91 1.44 0.00
Im2 0.78 1.56 0.24
Im3 0.82 1.63 0.14
Im4 0.89 1.46 0.03
Im5 0.66 1.78 0.42
Im6 0.96 1.15 0.01
Im7 0.34 0.72 1.69 0.31
Im10 0.93 1.32 0.00
Im11 0.57 1.71 0.57
Im12 0.89 1.22 0.13
Im13 0.72 1.76 0.31
Im14 0.77 1.68 0.22
Im16 0.68 2.03 0.33
Im17 0.88 1.65 0.00
Im18 0.70 1.84 0.32
Im19 0.64 2.71 0.30
Im20 0.86 1.19 0.19
Im21 0.73 1.44 0.36
Im22 0.79 1.56 0.22

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Factor loadings:

  • Number of items per factor >=3
    • this condition is respected in all cases except when we have 8 factors. We eliminate the 8 factor solution
  • 0.40–0.30–0.20 rule: satisfactory variables (a) load onto their primary factor above 0.40, (b) load onto alter-native factors below 0.30, and (c) demonstrate a difference of 0.20 between their primary and alternative factor loadings.
    • 5 factor solution:
      • this condition is not respected for many variables. We eliminate the 5 factor solution
    • 6 factor solution:
      • this condition is not respected for: Im6, Im7, Im9, (Im11), (Im15), Im16, Im17, Im18, Im19 where Im17 and Im18 are particularly spread out
    • 7 factor solution:
      • this condition is not respected for: Im7, Im8, Im9, Im15, Im16, Im19 where Im16 and Im19 are particularly spread out

Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables, potentially 19 as it also has the lower communality than Im16 and probably also factor 9 as it also has low communality

Thurstone simple structure criteria:

  • Each row (variable) of the factor pattern matrix should have at least one zero

  • Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors

  • For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other

  • When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns

  • For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns

2.2.4.4 PAF oblique Promax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()

i=1
for (n in nf) {
  # EFA_PAFn_obl[[i]] <- n
  EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA2, rotate="promax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn_obl) <- nf

length(EFA_PAFn_obl)
## [1] 4
2.2.4.4.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")

    EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))

    # Sort table
    EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
      setorder(cols = "Communality")
    
    # Display table  
    kbl <- EFA_PAFn_obl_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn_obl[[i]]$loadings["Im6",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im6 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im11 0.41
Im18 0.42
Im16 0.42
Im6 0.50
Im19 0.51
Im17 0.52
Im5 0.55
Im21 0.64
Im10 0.66
Im7 0.67
Im14 0.70
Im20 0.72
Im13 0.72
Im12 0.75
Im2 0.78
Im22 0.80
Im1 0.84
Im3 0.86
Im4 0.92

[1] “Communality for Im6 =0.547199381232095”

Number of factors = 6
Item Communality
Im16 0.42
Im11 0.45
Im19 0.51
Im5 0.55
Im6 0.64
Im21 0.64
Im18 0.65
Im13 0.69
Im10 0.71
Im7 0.73
Im12 0.74
Im14 0.74
Im20 0.78
Im22 0.79
Im2 0.80
Im17 0.83
Im3 0.86
Im1 0.89
Im4 0.92

[1] “Communality for Im6 =0.833006250441541”

Number of factors = 7
Item Communality
Im16 0.43
Im11 0.43
Im19 0.51
Im5 0.55
Im21 0.64
Im18 0.67
Im13 0.69
Im7 0.72
Im14 0.78
Im22 0.78
Im20 0.79
Im2 0.81
Im3 0.86
Im12 0.87
Im1 0.91
Im6 0.93
Im4 0.97
Im10 0.97
Im17 1.00

[1] “Communality for Im6 =0.971113915290573”

Number of factors = 8
Item Communality
Im11 0.43
Im5 0.58
Im21 0.64
Im16 0.67
Im18 0.68
Im13 0.69
Im7 0.69
Im19 0.70
Im2 0.76
Im14 0.78
Im22 0.78
Im20 0.81
Im3 0.86
Im12 0.87
Im4 0.97
Im6 0.99
Im10 1.00
Im17 1.00
Im1 1.00

[1] “Communality for Im6 =1.14058133882705”

2.2.4.4.2 Factor loadings
# loadings for all selected number of factors

test = list()

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}
Number of factors = 5
Variable MR1 MR2 MR5 MR4 MR3 Complexity Uniqueness
Im1 1.06 1.05 0.16
Im2 1.06 1.07 0.22
Im3 1.05 1.04 0.14
Im4 1.11 1.05 0.08
Im5 0.77 1.03 0.45
Im6 0.72 1.12 0.50
Im7 0.85 1.15 0.33
Im10 0.75 1.21 0.34
Im11 0.68 1.09 0.59
Im12 1.00 1.04 0.25
Im13 0.89 1.02 0.28
Im14 0.78 1.14 0.30
Im16 0.33 0.36 2.14 0.58
Im17 0.34 2.56 0.48
Im18 0.31 2.71 0.58
Im19 0.32 0.36 2.28 0.49
Im20 0.88 1.07 0.28
Im21 0.78 1.06 0.36
Im22 0.84 1.02 0.20
Number of factors = 6
Variable MR1 MR2 MR3 MR5 MR4 MR6 Complexity Uniqueness
Im1 1.04 1.05 0.11
Im2 1.00 1.04 0.20
Im3 1.02 1.05 0.14
Im4 1.08 1.05 0.08
Im5 0.76 1.03 0.45
Im6 0.84 1.39 0.36
Im7 0.91 1.18 0.27
Im10 0.68 1.69 0.29
Im11 0.67 1.05 0.55
Im12 0.91 1.06 0.26
Im13 0.77 1.22 0.31
Im14 0.71 1.55 0.26
Im16 0.33 0.33 2.12 0.58
Im17 0.77 1.14 0.17
Im18 0.69 1.14 0.35
Im19 0.33 2.58 0.49
Im20 0.91 1.08 0.22
Im21 0.75 1.06 0.36
Im22 0.80 1.04 0.21
Number of factors = 7
Variable MR1 MR3 MR5 MR4 MR2 MR6 MR7 Complexity Uniqueness
Im1 1.07 1.05 0.09
Im2 1.02 1.03 0.19
Im3 1.01 1.02 0.14
Im4 1.14 1.05 0.03
Im5 0.73 1.02 0.45
Im6 0.98 1.04 0.07
Im7 0.73 1.16 0.28
Im10 1.10 1.03 0.03
Im11 0.60 1.16 0.57
Im12 1.00 1.03 0.13
Im13 0.75 1.11 0.31
Im14 0.87 1.04 0.22
Im16 3.60 0.57
Im17 1.12 1.02 0.00
Im18 0.86 1.03 0.33
Im19 3.47 0.49
Im20 0.94 1.04 0.21
Im21 0.77 1.05 0.36
Im22 0.82 1.03 0.22
Number of factors = 8
Variable MR1 MR3 MR4 MR2 MR5 MR6 MR7 MR8 Complexity Uniqueness
Im1 1.03 1.01 0.00
Im2 0.86 1.01 0.24
Im3 0.90 1.02 0.14
Im4 1.02 1.03 0.03
Im5 0.73 1.09 0.42
Im6 1.06 1.03 0.01
Im7 0.72 1.14 0.31
Im10 1.05 1.02 0.00
Im11 0.60 1.15 0.57
Im12 1.02 1.04 0.13
Im13 0.75 1.09 0.31
Im14 0.82 1.03 0.22
Im16 0.80 1.02 0.33
Im17 1.03 1.01 0.00
Im18 0.81 1.00 0.32
Im19 0.72 1.04 0.30
Im20 0.97 1.09 0.19
Im21 0.77 1.05 0.36
Im22 0.82 1.04 0.22

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

2.3 Confirmatory factor analysis

We test whether the constructs found in the exploratory phase adequately describe what is going on.

2.3.1 6 factor model

# no excluded variables
CFA_model_img_6f <- "
DECO =~ Im3 + Im4 + Im5
FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
QUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
BRAND =~ Im17 + Im18 + Im9
"

# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "

# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "

# CFA_fit_img <- cfa(CFA_model_img_6f, data=data_img_EFA, missing="ML")
CFA_fit_img_6f <- cfa(CFA_model_img_6f, data=survey, missing="ML")

summary(CFA_fit_img_6f, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 110 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        81
## 
##   Number of observations                           553
##   Number of missing patterns                        87
## 
## Model Test User Model:
##                                                       
##   Test statistic                              1442.584
##   Degrees of freedom                               194
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              8838.959
##   Degrees of freedom                               231
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.855
##   Tucker-Lewis Index (TLI)                       0.827
##                                                       
##   Robust Comparative Fit Index (CFI)             0.854
##   Robust Tucker-Lewis Index (TLI)                0.827
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15479.697
##   Loglikelihood unrestricted model (H1)     -14758.405
##                                                       
##   Akaike (AIC)                               31121.394
##   Bayesian (BIC)                             31470.938
##   Sample-size adjusted Bayesian (SABIC)      31213.808
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.108
##   90 Percent confidence interval - lower         0.103
##   90 Percent confidence interval - upper         0.113
##   P-value H_0: RMSEA <= 0.050                    0.000
##   P-value H_0: RMSEA >= 0.080                    1.000
##                                                       
##   Robust RMSEA                                   0.110
##   90 Percent confidence interval - lower         0.105
##   90 Percent confidence interval - upper         0.116
##   P-value H_0: Robust RMSEA <= 0.050             0.000
##   P-value H_0: Robust RMSEA >= 0.080             1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.092
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.236    0.936
##     Im4               1.057    0.025   42.551    0.000    1.307    0.970
##     Im5               0.820    0.034   23.857    0.000    1.013    0.761
##   FRENCH =~                                                             
##     Im6               1.000                               0.642    0.535
##     Im7               1.219    0.106   11.525    0.000    0.783    0.644
##     Im8               1.244    0.099   12.567    0.000    0.799    0.755
##     Im10              1.251    0.095   13.133    0.000    0.803    0.914
##     Im14              1.244    0.095   13.142    0.000    0.799    0.929
##   ATMOS =~                                                              
##     Im20              1.000                               1.268    0.848
##     Im21              0.848    0.041   20.879    0.000    1.075    0.785
##     Im22              1.053    0.046   22.697    0.000    1.335    0.873
##   QUAL =~                                                               
##     Im11              1.000                               0.703    0.615
##     Im12              1.410    0.094   15.050    0.000    0.991    0.872
##     Im13              1.465    0.105   13.982    0.000    1.030    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.232    0.926
##     Im2               0.942    0.027   34.780    0.000    1.160    0.902
##     Im15              0.720    0.036   20.097    0.000    0.887    0.740
##     Im16              0.567    0.041   13.849    0.000    0.699    0.579
##     Im19              0.540    0.038   14.310    0.000    0.666    0.592
##   BRAND =~                                                              
##     Im17              1.000                               1.184    0.952
##     Im18              1.025    0.038   27.280    0.000    1.214    0.868
##     Im9               0.540    0.047   11.386    0.000    0.640    0.474
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FRENCH            0.344    0.046    7.416    0.000    0.434    0.434
##     ATMOS             0.730    0.082    8.901    0.000    0.466    0.466
##     QUAL              0.409    0.051    8.040    0.000    0.471    0.471
##     CHOICE            0.782    0.079    9.940    0.000    0.514    0.514
##     BRAND             0.778    0.076   10.268    0.000    0.531    0.531
##   FRENCH ~~                                                             
##     ATMOS             0.265    0.045    5.888    0.000    0.326    0.326
##     QUAL              0.206    0.030    6.812    0.000    0.456    0.456
##     CHOICE            0.299    0.044    6.737    0.000    0.378    0.378
##     BRAND             0.277    0.042    6.547    0.000    0.364    0.364
##   ATMOS ~~                                                              
##     QUAL              0.373    0.053    7.021    0.000    0.419    0.419
##     CHOICE            0.767    0.083    9.216    0.000    0.491    0.491
##     BRAND             0.792    0.081    9.797    0.000    0.528    0.528
##   QUAL ~~                                                               
##     CHOICE            0.460    0.054    8.585    0.000    0.531    0.531
##     BRAND             0.483    0.053    9.113    0.000    0.581    0.581
##   CHOICE ~~                                                             
##     BRAND             0.864    0.078   11.040    0.000    0.592    0.592
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.994    0.056   88.528    0.000    4.994    3.785
##    .Im4               4.997    0.057   86.919    0.000    4.997    3.709
##    .Im5               5.034    0.057   87.796    0.000    5.034    3.785
##    .Im6               5.824    0.051  113.338    0.000    5.824    4.849
##    .Im7               5.751    0.053  109.497    0.000    5.751    4.727
##    .Im8               6.000    0.045  133.008    0.000    6.000    5.671
##    .Im10              6.100    0.037  163.041    0.000    6.100    6.945
##    .Im14              6.139    0.037  166.909    0.000    6.139    7.138
##    .Im20              4.672    0.064   73.182    0.000    4.672    3.124
##    .Im21              5.139    0.058   87.973    0.000    5.139    3.751
##    .Im22              4.278    0.065   65.391    0.000    4.278    2.798
##    .Im11              5.653    0.049  115.277    0.000    5.653    4.943
##    .Im12              5.666    0.049  116.095    0.000    5.666    4.983
##    .Im13              5.448    0.052  105.630    0.000    5.448    4.525
##    .Im1               4.792    0.057   84.316    0.000    4.792    3.601
##    .Im2               4.861    0.055   88.357    0.000    4.861    3.779
##    .Im15              5.090    0.051   99.219    0.000    5.090    4.246
##    .Im16              5.130    0.052   98.387    0.000    5.130    4.251
##    .Im19              5.146    0.048  106.829    0.000    5.146    4.578
##    .Im17              5.025    0.053   94.490    0.000    5.025    4.038
##    .Im18              4.595    0.060   76.460    0.000    4.595    3.286
##    .Im9               5.075    0.058   87.318    0.000    5.075    3.757
##     DECO              0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     QUAL              0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.215    0.024    8.776    0.000    0.215    0.123
##    .Im4               0.108    0.024    4.439    0.000    0.108    0.060
##    .Im5               0.744    0.049   15.192    0.000    0.744    0.421
##    .Im6               1.030    0.066   15.665    0.000    1.030    0.714
##    .Im7               0.867    0.059   14.739    0.000    0.867    0.586
##    .Im8               0.482    0.034   14.159    0.000    0.482    0.430
##    .Im10              0.127    0.013    9.840    0.000    0.127    0.164
##    .Im14              0.101    0.012    8.329    0.000    0.101    0.137
##    .Im20              0.629    0.061   10.379    0.000    0.629    0.281
##    .Im21              0.721    0.057   12.668    0.000    0.721    0.384
##    .Im22              0.554    0.063    8.781    0.000    0.554    0.237
##    .Im11              0.814    0.055   14.805    0.000    0.814    0.622
##    .Im12              0.310    0.039    7.857    0.000    0.310    0.240
##    .Im13              0.390    0.044    8.777    0.000    0.390    0.269
##    .Im1               0.253    0.035    7.312    0.000    0.253    0.143
##    .Im2               0.308    0.033    9.422    0.000    0.308    0.186
##    .Im15              0.651    0.048   13.673    0.000    0.651    0.453
##    .Im16              0.968    0.065   14.927    0.000    0.968    0.664
##    .Im19              0.820    0.055   14.954    0.000    0.820    0.649
##    .Im17              0.146    0.036    4.039    0.000    0.146    0.094
##    .Im18              0.482    0.046   10.494    0.000    0.482    0.247
##    .Im9               1.415    0.089   15.908    0.000    1.415    0.776
##     DECO              1.527    0.107   14.308    0.000    1.000    1.000
##     FRENCH            0.412    0.064    6.422    0.000    1.000    1.000
##     ATMOS             1.608    0.138   11.683    0.000    1.000    1.000
##     QUAL              0.494    0.067    7.365    0.000    1.000    1.000
##     CHOICE            1.518    0.110   13.746    0.000    1.000    1.000
##     BRAND             1.402    0.100   14.036    0.000    1.000    1.000

2.3.1.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.3.1.2 local fit measures

# semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(CFA_fit_img_6f, what="std")$lambda
theta = inspect(CFA_fit_img_6f, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.3.1.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##      DECO FRENCH ATMOS  QUAL CHOICE BRAND
## Im3   NaN    NaN   NaN   NaN    NaN   NaN
## Im4   NaN    NaN   NaN   NaN    NaN   NaN
## Im5   NaN    NaN   NaN   NaN    NaN   NaN
## Im6   NaN  0.286   NaN   NaN    NaN   NaN
## Im7   NaN    NaN   NaN   NaN    NaN   NaN
## Im8   NaN    NaN   NaN   NaN    NaN   NaN
## Im10  NaN    NaN   NaN   NaN    NaN   NaN
## Im14  NaN    NaN   NaN   NaN    NaN   NaN
## Im20  NaN    NaN   NaN   NaN    NaN   NaN
## Im21  NaN    NaN   NaN   NaN    NaN   NaN
## Im22  NaN    NaN   NaN   NaN    NaN   NaN
## Im11  NaN    NaN   NaN 0.378    NaN   NaN
## Im12  NaN    NaN   NaN   NaN    NaN   NaN
## Im13  NaN    NaN   NaN   NaN    NaN   NaN
## Im1   NaN    NaN   NaN   NaN    NaN   NaN
## Im2   NaN    NaN   NaN   NaN    NaN   NaN
## Im15  NaN    NaN   NaN   NaN    NaN   NaN
## Im16  NaN    NaN   NaN   NaN  0.336   NaN
## Im19  NaN    NaN   NaN   NaN  0.351   NaN
## Im17  NaN    NaN   NaN   NaN    NaN   NaN
## Im18  NaN    NaN   NaN   NaN    NaN   NaN
## Im9   NaN    NaN   NaN   NaN    NaN 0.224
2.3.1.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO    NaN    NaN   NaN  NaN    NaN   NaN
## FRENCH  NaN    NaN   NaN  NaN    NaN   NaN
## ATMOS   NaN    NaN   NaN  NaN    NaN   NaN
## QUAL    NaN    NaN   NaN  NaN    NaN   NaN
## CHOICE  NaN    NaN   NaN  NaN    NaN   NaN
## BRAND   NaN    NaN   NaN  NaN    NaN   NaN
2.3.1.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO    NaN    NaN   NaN  NaN    NaN   NaN
## FRENCH  NaN    NaN   NaN  NaN    NaN   NaN
## ATMOS   NaN    NaN   NaN  NaN    NaN   NaN
## QUAL    NaN    NaN   NaN  NaN    NaN   NaN
## CHOICE  NaN    NaN   NaN  NaN    NaN   NaN
## BRAND   NaN    NaN   NaN  NaN    NaN   NaN
2.3.1.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_6f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO      1                               
## FRENCH  NaN      1                        
## ATMOS   NaN    NaN     1                  
## QUAL    NaN    NaN   NaN    1             
## CHOICE  NaN    NaN   NaN  NaN      1      
## BRAND   NaN    NaN   NaN  NaN    NaN     1
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##             DECO    FRENCH     ATMOS      QUAL    CHOICE     BRAND
## DECO   0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## FRENCH 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## ATMOS  0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## QUAL   0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## CHOICE 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## BRAND  0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
psi
##         DECO FRENCH ATMOS  QUAL CHOICE BRAND
## DECO   1.000                                
## FRENCH 0.434  1.000                         
## ATMOS  0.466  0.326 1.000                   
## QUAL   0.471  0.456 0.419 1.000             
## CHOICE 0.514  0.378 0.491 0.531  1.000      
## BRAND  0.531  0.364 0.528 0.581  0.592 1.000
AVEpsi_fail
##          DECO FRENCH  ATMOS   QUAL CHOICE  BRAND
## DECO        .                                   
## FRENCH    NaN      .                            
## ATMOS     NaN    NaN      .                     
## QUAL      NaN    NaN    NaN      .              
## CHOICE    NaN    NaN    NaN    NaN      .       
## BRAND     NaN    NaN    NaN    NaN -0.011      .

2.3.1.3 Modification indices

arrange(modificationindices(CFA_fit_img_6f),-mi)
##        lhs op  rhs      mi    epc sepc.lv sepc.all sepc.nox
## 1      Im1 ~~  Im2 495.934  0.951   0.951    3.408    3.408
## 2     Im10 ~~ Im14 298.631  0.357   0.357    3.154    3.154
## 3      Im6 ~~  Im7 255.917  0.693   0.693    0.734    0.734
## 4     Im16 ~~ Im19 128.231  0.463   0.463    0.519    0.519
## 5      Im7 ~~  Im8 104.366  0.316   0.316    0.489    0.489
## 6     DECO =~ Im19  76.462  0.344   0.424    0.378    0.378
## 7   FRENCH =~  Im9  73.482  0.783   0.503    0.372    0.372
## 8      Im6 ~~ Im10  55.895 -0.158  -0.158   -0.438   -0.438
## 9      Im1 ~~ Im16  55.410 -0.242  -0.242   -0.489   -0.489
## 10    QUAL =~ Im15  54.596  0.510   0.359    0.299    0.299
## 11     Im6 ~~  Im8  52.130  0.236   0.236    0.335    0.335
## 12     Im7 ~~ Im14  50.063 -0.145  -0.145   -0.491   -0.491
## 13  FRENCH =~ Im19  49.872  0.497   0.319    0.284    0.284
## 14    Im15 ~~ Im16  49.062  0.263   0.263    0.332    0.332
## 15     Im1 ~~ Im19  46.763 -0.204  -0.204   -0.449   -0.449
## 16    QUAL =~  Im9  45.834  0.702   0.494    0.365    0.365
## 17     Im2 ~~ Im19  45.384 -0.198  -0.198   -0.393   -0.393
## 18     Im7 ~~  Im9  45.214  0.340   0.340    0.307    0.307
## 19    DECO =~ Im16  44.633  0.288   0.356    0.295    0.295
## 20   BRAND =~ Im19  43.739  0.300   0.355    0.316    0.316
## 21     Im7 ~~ Im10  41.088 -0.134  -0.134   -0.406   -0.406
## 22    QUAL =~  Im2  38.006 -0.361  -0.254   -0.197   -0.197
## 23   BRAND =~ Im15  37.135  0.254   0.301    0.251    0.251
## 24    Im17 ~~ Im18  36.588  0.762   0.762    2.870    2.870
## 25     Im2 ~~ Im15  35.103 -0.179  -0.179   -0.399   -0.399
## 26    Im15 ~~ Im19  34.736  0.202   0.202    0.277    0.277
## 27    QUAL =~ Im19  33.294  0.434   0.305    0.271    0.271
## 28     Im8 ~~ Im14  32.038 -0.103  -0.103   -0.467   -0.467
## 29     Im6 ~~  Im9  31.342  0.301   0.301    0.249    0.249
## 30     Im1 ~~ Im15  30.586 -0.174  -0.174   -0.429   -0.429
## 31     Im2 ~~ Im16  28.333 -0.170  -0.170   -0.311   -0.311
## 32    DECO =~ Im15  27.803  0.191   0.236    0.197    0.197
## 33     Im6 ~~ Im14  27.360 -0.108  -0.108   -0.335   -0.335
## 34  FRENCH =~ Im16  27.263  0.403   0.259    0.214    0.214
## 35    DECO =~  Im2  26.666 -0.158  -0.195   -0.152   -0.152
## 36   ATMOS =~ Im15  24.669  0.181   0.230    0.192    0.192
## 37   BRAND =~ Im13  23.589  0.232   0.275    0.228    0.228
## 38    DECO =~  Im1  22.892 -0.149  -0.184   -0.138   -0.138
## 39   ATMOS =~  Im2  21.308 -0.142  -0.180   -0.140   -0.140
## 40    Im11 ~~ Im13  21.300 -0.191  -0.191   -0.339   -0.339
## 41   BRAND =~  Im2  21.047 -0.165  -0.195   -0.152   -0.152
## 42  FRENCH =~  Im1  20.125 -0.244  -0.156   -0.118   -0.118
## 43  FRENCH =~ Im15  18.582  0.279   0.179    0.149    0.149
## 44   BRAND =~ Im12  18.526 -0.197  -0.233   -0.205   -0.205
## 45   BRAND =~ Im16  17.630  0.209   0.247    0.205    0.205
## 46   BRAND =~  Im1  16.671 -0.150  -0.177   -0.133   -0.133
## 47   ATMOS =~ Im19  16.384  0.161   0.204    0.181    0.181
## 48   BRAND =~  Im6  14.589  0.161   0.191    0.159    0.159
## 49  CHOICE =~ Im20  14.430 -0.169  -0.208   -0.139   -0.139
## 50    Im14 ~~  Im9  13.864 -0.082  -0.082   -0.217   -0.217
## 51    Im11 ~~ Im12  13.374  0.145   0.145    0.289    0.289
## 52    Im21 ~~ Im22  13.217 -0.270  -0.270   -0.427   -0.427
## 53  CHOICE =~ Im13  13.044  0.152   0.187    0.155    0.155
## 54   ATMOS =~  Im7  12.806  0.134   0.170    0.140    0.140
## 55     Im8 ~~ Im10  12.666 -0.065  -0.065   -0.265   -0.265
## 56  FRENCH =~ Im11  12.345  0.269   0.173    0.151    0.151
## 57  CHOICE =~ Im12  11.541 -0.136  -0.168   -0.148   -0.148
## 58     Im3 ~~  Im4  11.447  0.264   0.264    1.735    1.735
## 59   ATMOS =~ Im16  11.243  0.146   0.185    0.153    0.153
## 60   ATMOS =~ Im12  11.072 -0.115  -0.146   -0.128   -0.128
## 61     Im8 ~~  Im9  10.943  0.125   0.125    0.152    0.152
## 62  FRENCH =~  Im2  10.891 -0.177  -0.114   -0.088   -0.088
## 63     Im7 ~~ Im22  10.253  0.126   0.126    0.182    0.182
## 64    DECO =~  Im9  10.194  0.167   0.207    0.153    0.153
## 65    Im11 ~~  Im9  10.067  0.156   0.156    0.145    0.145
## 66    Im15 ~~  Im9   9.926  0.139   0.139    0.145    0.145
## 67    QUAL =~ Im16   9.231  0.250   0.176    0.146    0.146
## 68     Im8 ~~ Im15   9.159  0.080   0.080    0.144    0.144
## 69   ATMOS =~  Im9   9.070  0.162   0.205    0.152    0.152
## 70    Im13 ~~ Im17   9.051  0.067   0.067    0.281    0.281
## 71     Im6 ~~ Im22   8.985  0.125   0.125    0.166    0.166
## 72    Im20 ~~ Im21   8.930  0.206   0.206    0.306    0.306
## 73   BRAND =~ Im22   8.880  0.147   0.175    0.114    0.114
## 74     Im8 ~~ Im16   8.801  0.095   0.095    0.139    0.139
## 75   BRAND =~ Im20   8.486 -0.141  -0.167   -0.111   -0.111
## 76   BRAND =~  Im7   8.244  0.114   0.135    0.111    0.111
## 77     Im3 ~~  Im1   8.143 -0.045  -0.045   -0.194   -0.194
## 78     Im8 ~~  Im2   7.823 -0.059  -0.059   -0.153   -0.153
## 79    QUAL =~ Im18   7.388 -0.230  -0.161   -0.115   -0.115
## 80    Im10 ~~ Im16   7.338  0.052   0.052    0.149    0.149
## 81    Im13 ~~  Im1   7.263  0.060   0.060    0.191    0.191
## 82     Im4 ~~ Im17   7.109 -0.041  -0.041   -0.322   -0.322
## 83    Im22 ~~ Im12   7.028 -0.078  -0.078   -0.189   -0.189
## 84    Im17 ~~  Im9   7.005 -0.112  -0.112   -0.247   -0.247
## 85    DECO =~  Im6   6.969  0.109   0.134    0.112    0.112
## 86   ATMOS =~ Im11   6.857  0.102   0.130    0.113    0.113
## 87  CHOICE =~  Im9   6.692  0.148   0.182    0.135    0.135
## 88   ATMOS =~  Im6   6.616  0.102   0.130    0.108    0.108
## 89    Im14 ~~  Im2   6.285  0.031   0.031    0.175    0.175
## 90   BRAND =~  Im5   6.246  0.103   0.122    0.092    0.092
## 91   BRAND =~  Im4   6.180 -0.071  -0.084   -0.062   -0.062
## 92    Im22 ~~  Im9   5.999  0.121   0.121    0.136    0.136
## 93    QUAL =~  Im5   5.978  0.169   0.119    0.089    0.089
## 94     Im1 ~~  Im9   5.822 -0.084  -0.084   -0.140   -0.140
## 95    QUAL =~  Im1   5.747 -0.143  -0.100   -0.075   -0.075
## 96  CHOICE =~ Im18   5.737 -0.115  -0.141   -0.101   -0.101
## 97     Im3 ~~  Im5   5.693 -0.084  -0.084   -0.209   -0.209
## 98     Im8 ~~ Im22   5.661  0.070   0.070    0.136    0.136
## 99    DECO =~ Im20   5.578 -0.100  -0.123   -0.082   -0.082
## 100  ATMOS =~  Im5   5.473  0.089   0.112    0.084    0.084
## 101   DECO =~ Im17   5.404 -0.091  -0.112   -0.090   -0.090
## 102   Im11 ~~ Im17   5.351 -0.061  -0.061   -0.177   -0.177
## 103 CHOICE =~  Im5   5.052  0.088   0.108    0.082    0.082
## 104 FRENCH =~ Im13   4.802 -0.157  -0.101   -0.084   -0.084
## 105   DECO =~ Im22   4.756  0.094   0.116    0.076    0.076
## 106   Im22 ~~ Im11   4.722  0.083   0.083    0.124    0.124
## 107 CHOICE =~ Im22   4.719  0.099   0.122    0.080    0.080
## 108   Im13 ~~ Im16   4.625 -0.073  -0.073   -0.118   -0.118
## 109   Im19 ~~ Im17   4.621  0.056   0.056    0.161    0.161
## 110  ATMOS =~ Im10   4.609 -0.038  -0.048   -0.055   -0.055
## 111  BRAND =~ Im10   4.570 -0.040  -0.048   -0.054   -0.054
## 112   Im14 ~~ Im22   4.494 -0.036  -0.036   -0.154   -0.154
## 113  ATMOS =~  Im4   4.422 -0.053  -0.067   -0.050   -0.050
## 114   Im14 ~~ Im15   4.415 -0.032  -0.032   -0.127   -0.127
## 115   Im21 ~~  Im9   4.370 -0.102  -0.102   -0.101   -0.101
## 116   Im10 ~~ Im13   4.362 -0.031  -0.031   -0.138   -0.138
## 117    Im7 ~~ Im15   4.358  0.074   0.074    0.098    0.098
## 118    Im3 ~~ Im22   4.300  0.047   0.047    0.135    0.135
## 119   Im20 ~~  Im1   4.283 -0.056  -0.056   -0.141   -0.141
## 120    Im4 ~~ Im16   4.262  0.048   0.048    0.149    0.149
## 121 FRENCH =~  Im5   4.167  0.144   0.093    0.070    0.070
## 122  ATMOS =~  Im8   4.061  0.057   0.072    0.068    0.068
## 123    Im6 ~~ Im20   4.039 -0.084  -0.084   -0.105   -0.105
## 124   Im10 ~~ Im11   4.002  0.036   0.036    0.111    0.111
## 125   Im20 ~~ Im17   3.990 -0.054  -0.054   -0.177   -0.177
## 126    Im6 ~~ Im11   3.977 -0.083  -0.083   -0.091   -0.091
## 127    Im5 ~~  Im1   3.869  0.051   0.051    0.117    0.117
## 128   Im15 ~~ Im17   3.695  0.045   0.045    0.147    0.147
## 129    Im4 ~~ Im18   3.604  0.035   0.035    0.152    0.152
## 130   Im12 ~~ Im15   3.556  0.050   0.050    0.110    0.110
## 131 FRENCH =~ Im17   3.536 -0.115  -0.074   -0.060   -0.060
## 132   Im14 ~~ Im16   3.474 -0.035  -0.035   -0.110   -0.110
## 133    Im3 ~~ Im15   3.381  0.037   0.037    0.099    0.099
## 134    Im3 ~~ Im17   3.375  0.029   0.029    0.161    0.161
## 135    Im3 ~~ Im19   3.371  0.040   0.040    0.096    0.096
## 136   Im13 ~~ Im15   3.338  0.051   0.051    0.102    0.102
## 137   Im22 ~~  Im1   3.275  0.049   0.049    0.132    0.132
## 138   Im20 ~~ Im13   3.270  0.057   0.057    0.115    0.115
## 139   Im13 ~~  Im2   3.219 -0.040  -0.040   -0.116   -0.116
## 140   Im11 ~~  Im1   3.071 -0.047  -0.047   -0.104   -0.104
## 141 CHOICE =~ Im21   3.048  0.074   0.091    0.066    0.066
## 142   Im10 ~~ Im17   3.000 -0.021  -0.021   -0.157   -0.157
## 143  ATMOS =~  Im1   2.962 -0.054  -0.068   -0.051   -0.051
## 144  ATMOS =~ Im13   2.889  0.062   0.078    0.065    0.065
## 145   Im16 ~~  Im9   2.810  0.089   0.089    0.076    0.076
## 146    Im5 ~~ Im14   2.794  0.028   0.028    0.101    0.101
## 147    Im4 ~~ Im22   2.701 -0.036  -0.036   -0.146   -0.146
## 148 CHOICE =~ Im10   2.670 -0.030  -0.037   -0.042   -0.042
## 149    Im1 ~~ Im17   2.662 -0.031  -0.031   -0.161   -0.161
## 150  ATMOS =~ Im14   2.649 -0.028  -0.035   -0.041   -0.041
## 151    Im4 ~~ Im19   2.526  0.034   0.034    0.113    0.113
## 152    Im4 ~~ Im11   2.492 -0.034  -0.034   -0.115   -0.115
## 153   Im21 ~~ Im18   2.456 -0.050  -0.050   -0.086   -0.086
## 154   Im12 ~~  Im2   2.343 -0.032  -0.032   -0.104   -0.104
## 155    Im6 ~~ Im15   2.316  0.057   0.057    0.070    0.070
## 156   Im12 ~~  Im9   2.302  0.057   0.057    0.086    0.086
## 157   DECO =~ Im12   2.287 -0.054  -0.067   -0.059   -0.059
## 158    Im6 ~~  Im1   2.248 -0.044  -0.044   -0.087   -0.087
## 159    Im3 ~~ Im20   2.237 -0.034  -0.034   -0.091   -0.091
## 160   Im15 ~~ Im18   2.236 -0.043  -0.043   -0.077   -0.077
## 161    Im7 ~~  Im1   2.236 -0.042  -0.042   -0.089   -0.089
## 162    Im6 ~~ Im12   2.164 -0.047  -0.047   -0.083   -0.083
## 163   Im10 ~~ Im12   2.160  0.020   0.020    0.102    0.102
## 164    Im4 ~~  Im2   2.090 -0.022  -0.022   -0.123   -0.123
## 165    Im5 ~~  Im6   1.873 -0.055  -0.055   -0.063   -0.063
## 166    Im4 ~~  Im6   1.846  0.032   0.032    0.096    0.096
## 167   DECO =~ Im10   1.832 -0.025  -0.031   -0.035   -0.035
## 168   Im22 ~~  Im2   1.825 -0.037  -0.037   -0.090   -0.090
## 169   Im10 ~~ Im22   1.781 -0.024  -0.024   -0.090   -0.090
## 170   Im12 ~~ Im17   1.776 -0.028  -0.028   -0.131   -0.131
## 171    Im6 ~~ Im18   1.754  0.047   0.047    0.066    0.066
## 172   Im21 ~~ Im17   1.749  0.035   0.035    0.108    0.108
## 173    Im5 ~~ Im16   1.746 -0.052  -0.052   -0.062   -0.062
## 174    Im3 ~~ Im12   1.732 -0.023  -0.023   -0.087   -0.087
## 175   Im22 ~~ Im13   1.726 -0.041  -0.041   -0.089   -0.089
## 176   Im18 ~~  Im9   1.696 -0.060  -0.060   -0.073   -0.073
## 177  ATMOS =~ Im17   1.682 -0.052  -0.065   -0.053   -0.053
## 178   QUAL =~  Im4   1.672 -0.060  -0.042   -0.031   -0.031
## 179   Im20 ~~ Im19   1.649  0.048   0.048    0.067    0.067
## 180   Im20 ~~  Im2   1.631 -0.035  -0.035   -0.080   -0.080
## 181 FRENCH =~ Im18   1.599 -0.082  -0.052   -0.038   -0.038
## 182    Im4 ~~ Im12   1.546  0.021   0.021    0.113    0.113
## 183 CHOICE =~ Im17   1.544  0.057   0.071    0.057    0.057
## 184    Im6 ~~ Im19   1.483  0.050   0.050    0.055    0.055
## 185   Im12 ~~ Im16   1.481  0.038   0.038    0.070    0.070
## 186    Im7 ~~ Im16   1.479 -0.052  -0.052   -0.056   -0.056
## 187   DECO =~ Im13   1.462  0.045   0.056    0.046    0.046
## 188 FRENCH =~ Im20   1.442 -0.089  -0.057   -0.038   -0.038
## 189   Im12 ~~ Im13   1.442  0.089   0.089    0.255    0.255
## 190  BRAND =~  Im3   1.434  0.033   0.039    0.030    0.030
## 191   Im12 ~~  Im1   1.360 -0.024  -0.024   -0.087   -0.087
## 192    Im3 ~~ Im18   1.301 -0.022  -0.022   -0.067   -0.067
## 193   Im16 ~~ Im17   1.269  0.032   0.032    0.085    0.085
## 194    Im3 ~~ Im11   1.261  0.025   0.025    0.060    0.060
## 195   Im14 ~~ Im17   1.252  0.013   0.013    0.110    0.110
## 196   Im10 ~~ Im19   1.233  0.019   0.019    0.060    0.060
## 197    Im3 ~~ Im10   1.230  0.012   0.012    0.070    0.070
## 198    Im8 ~~ Im18   1.200 -0.027  -0.027   -0.057   -0.057
## 199    Im8 ~~  Im1   1.194 -0.023  -0.023   -0.065   -0.065
## 200   Im21 ~~  Im2   1.185  0.030   0.030    0.063    0.063
## 201   QUAL =~ Im22   1.168 -0.084  -0.059   -0.038   -0.038
## 202 CHOICE =~ Im14   1.154  0.019   0.023    0.027    0.027
## 203   Im10 ~~  Im9   1.119  0.024   0.024    0.057    0.057
## 204   DECO =~ Im18   1.115  0.043   0.053    0.038    0.038
## 205 CHOICE =~  Im4   1.111 -0.028  -0.035   -0.026   -0.026
## 206   Im14 ~~ Im21   1.104  0.018   0.018    0.067    0.067
## 207    Im5 ~~ Im19   1.093 -0.038  -0.038   -0.048   -0.048
## 208    Im4 ~~  Im8   1.089  0.017   0.017    0.076    0.076
## 209   Im22 ~~ Im18   1.078  0.034   0.034    0.065    0.065
## 210   Im22 ~~ Im15   1.067  0.036   0.036    0.059    0.059
## 211   Im13 ~~ Im18   1.031 -0.027  -0.027   -0.062   -0.062
## 212 CHOICE =~  Im7   0.941  0.037   0.046    0.038    0.038
## 213    Im4 ~~ Im10   0.906 -0.010  -0.010   -0.082   -0.082
## 214    Im3 ~~ Im14   0.890 -0.010  -0.010   -0.065   -0.065
## 215   Im10 ~~  Im2   0.889 -0.012  -0.012   -0.061   -0.061
## 216  ATMOS =~  Im3   0.869  0.023   0.029    0.022    0.022
## 217   Im11 ~~ Im16   0.846  0.038   0.038    0.043    0.043
## 218   QUAL =~ Im14   0.840  0.031   0.022    0.026    0.026
## 219   QUAL =~ Im20   0.837  0.069   0.049    0.033    0.033
## 220    Im1 ~~ Im18   0.830  0.021   0.021    0.060    0.060
## 221    Im3 ~~ Im16   0.818  0.022   0.022    0.048    0.048
## 222   DECO =~  Im7   0.814  0.035   0.043    0.036    0.036
## 223    Im2 ~~ Im18   0.811 -0.021  -0.021   -0.054   -0.054
## 224   Im20 ~~ Im12   0.794  0.026   0.026    0.059    0.059
## 225 FRENCH =~ Im22   0.781  0.067   0.043    0.028    0.028
## 226   Im20 ~~ Im16   0.767  0.036   0.036    0.046    0.046
## 227   Im14 ~~ Im18   0.739 -0.012  -0.012   -0.056   -0.056
## 228   Im22 ~~ Im19   0.717 -0.032  -0.032   -0.047   -0.047
## 229   QUAL =~ Im10   0.654 -0.028  -0.020   -0.023   -0.023
## 230   Im14 ~~ Im13   0.649  0.011   0.011    0.057    0.057
## 231   Im14 ~~ Im11   0.639  0.014   0.014    0.048    0.048
## 232 CHOICE =~  Im6   0.612  0.032   0.039    0.033    0.033
## 233   Im19 ~~  Im9   0.595  0.037   0.037    0.035    0.035
## 234  BRAND =~ Im11   0.591 -0.036  -0.043   -0.038   -0.038
## 235    Im6 ~~  Im2   0.577 -0.023  -0.023   -0.040   -0.040
## 236   Im20 ~~ Im15   0.576  0.026   0.026    0.041    0.041
## 237    Im5 ~~ Im22   0.561  0.027   0.027    0.043    0.043
## 238    Im8 ~~ Im19   0.558  0.022   0.022    0.035    0.035
## 239    Im8 ~~ Im21   0.538 -0.022  -0.022   -0.037   -0.037
## 240   Im21 ~~ Im12   0.537  0.021   0.021    0.045    0.045
## 241   Im11 ~~ Im19   0.536  0.028   0.028    0.034    0.034
## 242   Im21 ~~  Im1   0.534  0.020   0.020    0.046    0.046
## 243   QUAL =~  Im7   0.517  0.053   0.037    0.031    0.031
## 244   Im10 ~~ Im18   0.516  0.011   0.011    0.044    0.044
## 245    Im5 ~~ Im11   0.511  0.026   0.026    0.034    0.034
## 246   Im10 ~~ Im20   0.483  0.012   0.012    0.044    0.044
## 247   Im12 ~~ Im18   0.465 -0.017  -0.017   -0.044   -0.044
## 248   Im14 ~~  Im1   0.460  0.008   0.008    0.052    0.052
## 249 FRENCH =~  Im3   0.457 -0.031  -0.020   -0.015   -0.015
## 250   Im20 ~~ Im11   0.453  0.026   0.026    0.036    0.036
## 251    Im3 ~~  Im8   0.442 -0.012  -0.012   -0.036   -0.036
## 252   Im20 ~~ Im18   0.417  0.021   0.021    0.038    0.038
## 253   Im20 ~~ Im22   0.407  0.061   0.061    0.103    0.103
## 254   Im10 ~~  Im1   0.405 -0.008  -0.008   -0.045   -0.045
## 255    Im5 ~~ Im20   0.402  0.023   0.023    0.034    0.034
## 256  BRAND =~ Im14   0.390 -0.011  -0.014   -0.016   -0.016
## 257    Im2 ~~  Im9   0.381 -0.022  -0.022   -0.033   -0.033
## 258   Im21 ~~ Im11   0.373 -0.023  -0.023   -0.030   -0.030
## 259   Im16 ~~ Im18   0.357 -0.021  -0.021   -0.030   -0.030
## 260    Im5 ~~ Im15   0.339 -0.019  -0.019   -0.028   -0.028
## 261   Im21 ~~ Im13   0.328 -0.018  -0.018   -0.034   -0.034
## 262   QUAL =~  Im8   0.320 -0.031  -0.022   -0.021   -0.021
## 263    Im5 ~~ Im21   0.319 -0.021  -0.021   -0.028   -0.028
## 264   DECO =~  Im8   0.317  0.016   0.020    0.019    0.019
## 265    Im7 ~~ Im19   0.317  0.022   0.022    0.026    0.026
## 266    Im4 ~~ Im20   0.315  0.012   0.012    0.047    0.047
## 267   Im11 ~~  Im2   0.310  0.015   0.015    0.030    0.030
## 268    Im5 ~~  Im8   0.298 -0.015  -0.015   -0.026   -0.026
## 269    Im7 ~~ Im20   0.292 -0.021  -0.021   -0.029   -0.029
## 270    Im4 ~~ Im13   0.275 -0.009  -0.009   -0.045   -0.045
## 271    Im3 ~~ Im13   0.274  0.010   0.010    0.033    0.033
## 272    Im8 ~~ Im13   0.252 -0.012  -0.012   -0.028   -0.028
## 273   DECO =~ Im11   0.240  0.019   0.024    0.021    0.021
## 274   Im12 ~~ Im19   0.218  0.013   0.013    0.027    0.027
## 275    Im4 ~~  Im5   0.193  0.017   0.017    0.059    0.059
## 276    Im3 ~~  Im7   0.193 -0.010  -0.010   -0.024   -0.024
## 277    Im7 ~~ Im12   0.191 -0.013  -0.013   -0.025   -0.025
## 278    Im5 ~~ Im17   0.190  0.011   0.011    0.033    0.033
## 279    Im7 ~~ Im21   0.188 -0.017  -0.017   -0.022   -0.022
## 280    Im5 ~~  Im9   0.179  0.020   0.020    0.019    0.019
## 281   Im19 ~~ Im18   0.174 -0.013  -0.013   -0.021   -0.021
## 282   Im21 ~~ Im16   0.170 -0.017  -0.017   -0.020   -0.020
## 283 FRENCH =~  Im4   0.152 -0.018  -0.012   -0.009   -0.009
## 284    Im4 ~~ Im15   0.151 -0.008  -0.008   -0.028   -0.028
## 285   Im21 ~~ Im19   0.149 -0.014  -0.014   -0.019   -0.019
## 286   DECO =~ Im14   0.132 -0.007  -0.008   -0.009   -0.009
## 287    Im4 ~~  Im1   0.125  0.005   0.005    0.033    0.033
## 288    Im3 ~~  Im2   0.124  0.006   0.006    0.022    0.022
## 289    Im2 ~~ Im17   0.116  0.006   0.006    0.031    0.031
## 290   Im10 ~~ Im15   0.108 -0.005  -0.005   -0.018   -0.018
## 291    Im5 ~~ Im10   0.106 -0.006  -0.006   -0.018   -0.018
## 292 FRENCH =~ Im21   0.106  0.023   0.015    0.011    0.011
## 293    Im6 ~~ Im16   0.097 -0.014  -0.014   -0.014   -0.014
## 294 CHOICE =~  Im8   0.094 -0.009  -0.011   -0.010   -0.010
## 295    Im7 ~~ Im11   0.091 -0.012  -0.012   -0.014   -0.014
## 296   Im10 ~~ Im21   0.089 -0.005  -0.005   -0.018   -0.018
## 297   Im11 ~~ Im18   0.089  0.010   0.010    0.015    0.015
## 298    Im5 ~~  Im2   0.087 -0.008  -0.008   -0.016   -0.016
## 299    Im7 ~~ Im18   0.086 -0.010  -0.010   -0.015   -0.015
## 300   QUAL =~  Im6   0.086 -0.023  -0.016   -0.013   -0.013
## 301    Im5 ~~ Im12   0.084  0.008   0.008    0.017    0.017
## 302 CHOICE =~ Im11   0.082 -0.012  -0.015   -0.013   -0.013
## 303    Im8 ~~ Im12   0.076 -0.006  -0.006   -0.016   -0.016
## 304    Im6 ~~ Im13   0.071  0.009   0.009    0.014    0.014
## 305   Im14 ~~ Im20   0.068 -0.004  -0.004   -0.018   -0.018
## 306    Im5 ~~  Im7   0.064  0.010   0.010    0.012    0.012
## 307   Im22 ~~ Im17   0.054  0.006   0.006    0.022    0.022
## 308    Im6 ~~ Im21   0.052 -0.010  -0.010   -0.011   -0.011
## 309   QUAL =~ Im21   0.051  0.016   0.011    0.008    0.008
## 310    Im4 ~~ Im21   0.046  0.005   0.005    0.017    0.017
## 311   Im21 ~~ Im15   0.040 -0.007  -0.007   -0.010   -0.010
## 312   Im14 ~~ Im12   0.039 -0.003  -0.003   -0.015   -0.015
## 313    Im7 ~~ Im13   0.037 -0.006  -0.006   -0.011   -0.011
## 314    Im8 ~~ Im17   0.036 -0.004  -0.004   -0.015   -0.015
## 315   QUAL =~ Im17   0.035 -0.015  -0.011   -0.009   -0.009
## 316  BRAND =~ Im21   0.027 -0.007  -0.009   -0.006   -0.006
## 317   Im14 ~~ Im19   0.027  0.003   0.003    0.010    0.010
## 318   Im20 ~~  Im9   0.021  0.007   0.007    0.008    0.008
## 319    Im7 ~~ Im17   0.021 -0.004  -0.004   -0.011   -0.011
## 320  BRAND =~  Im8   0.020  0.004   0.005    0.005    0.005
## 321 CHOICE =~  Im3   0.018 -0.004  -0.004   -0.003   -0.003
## 322    Im3 ~~  Im9   0.018 -0.004  -0.004   -0.007   -0.007
## 323    Im5 ~~ Im18   0.017  0.004   0.004    0.007    0.007
## 324   DECO =~ Im21   0.017  0.005   0.006    0.005    0.005
## 325    Im8 ~~ Im20   0.014  0.003   0.003    0.006    0.006
## 326    Im4 ~~  Im9   0.014 -0.003  -0.003   -0.008   -0.008
## 327    Im3 ~~ Im21   0.010 -0.002  -0.002   -0.006   -0.006
## 328  ATMOS =~ Im18   0.009  0.004   0.005    0.004    0.004
## 329   Im11 ~~ Im15   0.007 -0.003  -0.003   -0.004   -0.004
## 330    Im7 ~~  Im2   0.006 -0.002  -0.002   -0.004   -0.004
## 331 FRENCH =~ Im12   0.002 -0.003  -0.002   -0.002   -0.002
## 332   Im13 ~~  Im9   0.002  0.002   0.002    0.003    0.003
## 333    Im4 ~~ Im14   0.002  0.000   0.000   -0.004   -0.004
## 334    Im4 ~~  Im7   0.002 -0.001  -0.001   -0.003   -0.003
## 335    Im8 ~~ Im11   0.002  0.001   0.001    0.002    0.002
## 336   Im13 ~~ Im19   0.002  0.001   0.001    0.002    0.002
## 337    Im3 ~~  Im6   0.002  0.001   0.001    0.002    0.002
## 338   Im22 ~~ Im16   0.001  0.001   0.001    0.002    0.002
## 339   QUAL =~  Im3   0.001  0.001   0.001    0.001    0.001
## 340    Im6 ~~ Im17   0.000  0.000   0.000   -0.001   -0.001
## 341    Im5 ~~ Im13   0.000  0.000   0.000    0.000    0.000

2.3.2 7 factor model

Based on the modification indices we create a new model

# # no excluded variables:
# CFA_model_img_7f <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7 + Im9
# "

# MIs indicate separate Im1, Im2 and Im16, Im19 no excluded variables
# Im8 under FRENCH
# exclude Im8 
# exclude Im15
# exclude Im9
CFA_model_img_7f <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
"

# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "

# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "

# # 8 factor model: excluded variables: Im9, Im15, Im8, Im11
# CFA_model_img_7f <- "
# QUAL =~ Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# PROF =~ Im16 + Im19
# "


CFA_fit_img_7f <- cfa(CFA_model_img_7f, data=survey, missing="ML")
summary(CFA_fit_img_7f, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 108 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        85
## 
##   Number of observations                           553
##   Number of missing patterns                        79
## 
## Model Test User Model:
##                                                       
##   Test statistic                               259.047
##   Degrees of freedom                               124
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              7474.765
##   Degrees of freedom                               171
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.982
##   Tucker-Lewis Index (TLI)                       0.975
##                                                       
##   Robust Comparative Fit Index (CFI)             0.981
##   Robust Tucker-Lewis Index (TLI)                0.974
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12973.111
##   Loglikelihood unrestricted model (H1)     -12843.588
##                                                       
##   Akaike (AIC)                               26116.223
##   Bayesian (BIC)                             26483.028
##   Sample-size adjusted Bayesian (SABIC)      26213.200
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.044
##   90 Percent confidence interval - lower         0.037
##   90 Percent confidence interval - upper         0.052
##   P-value H_0: RMSEA <= 0.050                    0.886
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   0.045
##   90 Percent confidence interval - lower         0.038
##   90 Percent confidence interval - upper         0.053
##   P-value H_0: Robust RMSEA <= 0.050             0.825
##   P-value H_0: Robust RMSEA >= 0.080             0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.029
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.236    0.937
##     Im4               1.056    0.025   42.717    0.000    1.305    0.969
##     Im5               0.818    0.034   23.815    0.000    1.011    0.760
##   FOOD =~                                                               
##     Im10              1.000                               0.812    0.923
##     Im14              1.015    0.036   28.479    0.000    0.824    0.952
##   ATMOS =~                                                              
##     Im20              1.000                               1.265    0.845
##     Im21              0.849    0.041   20.823    0.000    1.074    0.783
##     Im22              1.060    0.047   22.606    0.000    1.340    0.877
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.703    0.615
##     Im12              1.410    0.094   15.046    0.000    0.991    0.872
##     Im13              1.465    0.105   13.968    0.000    1.030    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.305    0.980
##     Im2               0.885    0.033   27.043    0.000    1.155    0.899
##   PROF =~                                                               
##     Im16              1.000                               0.921    0.766
##     Im19              1.046    0.061   17.170    0.000    0.963    0.856
##   BRAND =~                                                              
##     Im17              1.000                               1.204    0.969
##     Im18              0.994    0.041   24.143    0.000    1.197    0.856
##   FRENCH =~                                                             
##     Im6               1.000                               0.975    0.813
##     Im7               1.184    0.071   16.770    0.000    1.155    0.955
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.418    0.050    8.393    0.000    0.416    0.416
##     ATMOS             0.730    0.082    8.912    0.000    0.467    0.467
##     PRODQUAL          0.409    0.051    8.040    0.000    0.471    0.471
##     CHOICE            0.711    0.079    9.032    0.000    0.441    0.441
##     PROF              0.743    0.071   10.465    0.000    0.653    0.653
##     BRAND             0.770    0.076   10.140    0.000    0.517    0.517
##     FRENCH            0.402    0.063    6.350    0.000    0.334    0.334
##   FOOD ~~                                                               
##     ATMOS             0.303    0.051    5.948    0.000    0.295    0.295
##     PRODQUAL          0.258    0.034    7.662    0.000    0.452    0.452
##     CHOICE            0.328    0.050    6.584    0.000    0.309    0.309
##     PROF              0.372    0.043    8.589    0.000    0.498    0.498
##     BRAND             0.318    0.047    6.801    0.000    0.325    0.325
##     FRENCH            0.463    0.047    9.829    0.000    0.585    0.585
##   ATMOS ~~                                                              
##     PRODQUAL          0.372    0.053    7.011    0.000    0.418    0.418
##     CHOICE            0.739    0.085    8.728    0.000    0.448    0.448
##     PROF              0.557    0.069    8.089    0.000    0.478    0.478
##     BRAND             0.787    0.081    9.715    0.000    0.516    0.516
##     FRENCH            0.410    0.065    6.352    0.000    0.333    0.333
##   PRODQUAL ~~                                                           
##     CHOICE            0.439    0.054    8.161    0.000    0.478    0.478
##     PROF              0.343    0.043    7.946    0.000    0.529    0.529
##     BRAND             0.479    0.053    9.046    0.000    0.566    0.566
##     FRENCH            0.210    0.037    5.622    0.000    0.306    0.306
##   CHOICE ~~                                                             
##     PROF              0.717    0.072    9.956    0.000    0.597    0.597
##     BRAND             0.817    0.079   10.362    0.000    0.519    0.519
##     FRENCH            0.286    0.060    4.735    0.000    0.225    0.225
##   PROF ~~                                                               
##     BRAND             0.667    0.066   10.040    0.000    0.601    0.601
##     FRENCH            0.328    0.051    6.438    0.000    0.366    0.366
##   BRAND ~~                                                              
##     FRENCH            0.378    0.061    6.175    0.000    0.322    0.322
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.995    0.056   88.560    0.000    4.995    3.786
##    .Im4               4.999    0.057   86.983    0.000    4.999    3.712
##    .Im5               5.035    0.057   87.844    0.000    5.035    3.787
##    .Im10              6.100    0.037  162.789    0.000    6.100    6.937
##    .Im14              6.138    0.037  165.861    0.000    6.138    7.093
##    .Im20              4.672    0.064   73.177    0.000    4.672    3.123
##    .Im21              5.139    0.058   87.970    0.000    5.139    3.751
##    .Im22              4.279    0.065   65.401    0.000    4.279    2.799
##    .Im11              5.653    0.049  115.271    0.000    5.653    4.943
##    .Im12              5.666    0.049  116.089    0.000    5.666    4.983
##    .Im13              5.448    0.052  105.615    0.000    5.448    4.524
##    .Im1               4.790    0.057   84.202    0.000    4.790    3.597
##    .Im2               4.857    0.055   88.354    0.000    4.857    3.779
##    .Im16              5.135    0.052   99.147    0.000    5.135    4.269
##    .Im19              5.145    0.048  106.948    0.000    5.145    4.574
##    .Im17              5.025    0.053   94.519    0.000    5.025    4.041
##    .Im18              4.595    0.060   76.447    0.000    4.595    3.287
##    .Im6               5.827    0.051  113.784    0.000    5.827    4.858
##    .Im7               5.753    0.052  110.826    0.000    5.753    4.756
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.213    0.024    8.755    0.000    0.213    0.122
##    .Im4               0.109    0.024    4.532    0.000    0.109    0.060
##    .Im5               0.747    0.049   15.217    0.000    0.747    0.422
##    .Im10              0.114    0.019    5.961    0.000    0.114    0.148
##    .Im14              0.070    0.019    3.680    0.000    0.070    0.093
##    .Im20              0.638    0.061   10.451    0.000    0.638    0.285
##    .Im21              0.725    0.057   12.672    0.000    0.725    0.386
##    .Im22              0.541    0.063    8.539    0.000    0.541    0.231
##    .Im11              0.814    0.055   14.802    0.000    0.814    0.622
##    .Im12              0.310    0.040    7.845    0.000    0.310    0.240
##    .Im13              0.390    0.045    8.765    0.000    0.390    0.269
##    .Im1               0.070    0.050    1.394    0.163    0.070    0.040
##    .Im2               0.317    0.044    7.233    0.000    0.317    0.192
##    .Im16              0.599    0.052   11.498    0.000    0.599    0.414
##    .Im19              0.338    0.045    7.457    0.000    0.338    0.267
##    .Im17              0.095    0.045    2.112    0.035    0.095    0.062
##    .Im18              0.521    0.055    9.540    0.000    0.521    0.267
##    .Im6               0.487    0.056    8.677    0.000    0.487    0.339
##    .Im7               0.128    0.067    1.930    0.054    0.128    0.088
##     DECO              1.528    0.107   14.326    0.000    1.000    1.000
##     FOOD              0.659    0.049   13.328    0.000    1.000    1.000
##     ATMOS             1.599    0.138   11.623    0.000    1.000    1.000
##     PRODQUAL          0.494    0.067    7.361    0.000    1.000    1.000
##     CHOICE            1.704    0.118   14.388    0.000    1.000    1.000
##     PROF              0.849    0.088    9.638    0.000    1.000    1.000
##     BRAND             1.451    0.104   13.988    0.000    1.000    1.000
##     FRENCH            0.952    0.095   10.058    0.000    1.000    1.000

2.3.2.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.3.2.2 local fit measures

# semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(CFA_fit_img_7f, what="std")$lambda
theta = inspect(CFA_fit_img_7f, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.3.2.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##      DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## Im3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im5   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im10  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im14  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im20  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im21  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im22  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im11  NaN  NaN   NaN  0.378    NaN  NaN   NaN    NaN
## Im12  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im13  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im16  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im19  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im17  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im18  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im6   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im7   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
2.3.2.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
2.3.2.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
2.3.2.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_7f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##          DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO        1                                           
## FOOD      NaN    1                                      
## ATMOS     NaN  NaN     1                                
## PRODQUAL  NaN  NaN   NaN      1                         
## CHOICE    NaN  NaN   NaN    NaN      1                  
## PROF      NaN  NaN   NaN    NaN    NaN    1             
## BRAND     NaN  NaN   NaN    NaN    NaN  NaN     1       
## FRENCH    NaN  NaN   NaN    NaN    NaN  NaN   NaN      1
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##               DECO      FOOD     ATMOS PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FOOD     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## ATMOS    0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PRODQUAL 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## CHOICE   0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PROF     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## BRAND    0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH   0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
##            FRENCH
## DECO     0.786707
## FOOD     0.786707
## ATMOS    0.786707
## PRODQUAL 0.786707
## CHOICE   0.786707
## PROF     0.786707
## BRAND    0.786707
## FRENCH   0.786707
psi
##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH
## DECO     1.000                                             
## FOOD     0.416 1.000                                       
## ATMOS    0.467 0.295 1.000                                 
## PRODQUAL 0.471 0.452 0.418  1.000                          
## CHOICE   0.441 0.309 0.448  0.478  1.000                   
## PROF     0.653 0.498 0.478  0.529  0.597 1.000             
## BRAND    0.517 0.325 0.516  0.566  0.519 0.601 1.000       
## FRENCH   0.334 0.585 0.333  0.306  0.225 0.366 0.322  1.000
AVEpsi_fail
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH
## DECO          .                                                 
## FOOD        NaN      .                                          
## ATMOS       NaN    NaN      .                                   
## PRODQUAL    NaN    NaN    NaN      .                            
## CHOICE      NaN    NaN    NaN    NaN      .                     
## PROF        NaN    NaN    NaN    NaN    NaN      .              
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .       
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .

2.3.2.3 Modification indices

arrange(modificationindices(CFA_fit_img_7f),-mi)
##          lhs op  rhs     mi    epc sepc.lv sepc.all sepc.nox
## 1      BRAND =~ Im13 23.832  0.220   0.265    0.220    0.220
## 2       Im11 ~~ Im13 21.323 -0.191  -0.191   -0.338   -0.338
## 3      BRAND =~ Im12 17.245 -0.179  -0.216   -0.190   -0.190
## 4       Im21 ~~ Im22 15.139 -0.285  -0.285   -0.455   -0.455
## 5     CHOICE =~ Im20 14.777 -0.151  -0.197   -0.132   -0.132
## 6     CHOICE =~ Im13 13.970  0.133   0.174    0.144    0.144
## 7       Im11 ~~ Im12 13.307  0.145   0.145    0.288    0.288
## 8       FOOD =~ Im11 12.742  0.215   0.174    0.152    0.152
## 9       Im20 ~~ Im21 11.455  0.228   0.228    0.335    0.335
## 10     ATMOS =~ Im12 10.952 -0.115  -0.145   -0.127   -0.127
## 11      Im13 ~~  Im1 10.707  0.068   0.068    0.409    0.409
## 12    CHOICE =~ Im12 10.663 -0.111  -0.145   -0.127   -0.127
## 13      Im13 ~~ Im17  9.392  0.068   0.068    0.355    0.355
## 14       Im4 ~~ Im17  9.096 -0.046  -0.046   -0.446   -0.446
## 15     BRAND =~ Im20  8.230 -0.133  -0.160   -0.107   -0.107
## 16      Im10 ~~ Im16  7.956  0.046   0.046    0.175    0.175
## 17     BRAND =~ Im22  7.656  0.131   0.158    0.103    0.103
## 18    FRENCH =~ Im22  7.278  0.136   0.132    0.087    0.087
## 19     ATMOS =~ Im11  6.691  0.101   0.128    0.112    0.112
## 20      Im22 ~~ Im12  6.644 -0.076  -0.076   -0.185   -0.185
## 21    CHOICE =~  Im5  6.302  0.086   0.112    0.084    0.084
## 22     BRAND =~  Im4  6.247 -0.067  -0.081   -0.060   -0.060
## 23  PRODQUAL =~  Im5  6.120  0.171   0.120    0.091    0.091
## 24      Im14 ~~ Im16  6.048 -0.039  -0.039   -0.191   -0.191
## 25      Im10 ~~  Im6  6.011 -0.035  -0.035   -0.147   -0.147
## 26     BRAND =~  Im5  5.755  0.095   0.115    0.086    0.086
## 27       Im3 ~~  Im1  5.614 -0.034  -0.034   -0.281   -0.281
## 28      DECO =~  Im7  5.531 -0.093  -0.114   -0.095   -0.095
## 29      DECO =~  Im6  5.531  0.078   0.097    0.080    0.080
## 30     ATMOS =~  Im5  5.517  0.089   0.113    0.085    0.085
## 31      DECO =~ Im18  5.361  0.099   0.123    0.088    0.088
## 32      DECO =~ Im17  5.361 -0.100  -0.124   -0.099   -0.099
## 33    FRENCH =~ Im20  5.231 -0.113  -0.111   -0.074   -0.074
## 34      Im22 ~~ Im11  5.182  0.087   0.087    0.131    0.131
## 35      FOOD =~ Im13  5.137 -0.127  -0.103   -0.086   -0.086
## 36       Im3 ~~  Im4  5.131  0.162   0.162    1.061    1.061
## 37      DECO =~ Im20  5.124 -0.096  -0.118   -0.079   -0.079
## 38     BRAND =~  Im7  5.064 -0.090  -0.108   -0.089   -0.089
## 39     BRAND =~  Im6  5.064  0.076   0.091    0.076    0.076
## 40      Im22 ~~  Im1  5.051  0.056   0.056    0.290    0.290
## 41      Im13 ~~ Im16  5.040 -0.067  -0.067   -0.138   -0.138
## 42      Im11 ~~  Im6  4.965 -0.069  -0.069   -0.109   -0.109
## 43      Im10 ~~ Im13  4.793 -0.031  -0.031   -0.146   -0.146
## 44       Im4 ~~ Im18  4.776  0.040   0.040    0.166    0.166
## 45       Im5 ~~  Im6  4.758 -0.065  -0.065   -0.108   -0.108
## 46       Im3 ~~ Im22  4.749  0.049   0.049    0.143    0.143
## 47      Im10 ~~  Im7  4.706  0.032   0.032    0.265    0.265
## 48    CHOICE =~ Im22  4.697  0.087   0.113    0.074    0.074
## 49       Im3 ~~  Im5  4.674 -0.071  -0.071   -0.178   -0.178
## 50      Im13 ~~  Im2  4.562 -0.044  -0.044   -0.125   -0.125
## 51      FOOD =~  Im5  4.520  0.117   0.095    0.072    0.072
## 52      Im20 ~~ Im17  4.488 -0.057  -0.057   -0.230   -0.230
## 53     ATMOS =~  Im4  4.309 -0.052  -0.066   -0.049   -0.049
## 54      DECO =~ Im22  4.302  0.090   0.111    0.072    0.072
## 55      PROF =~  Im2  4.223  0.170   0.157    0.122    0.122
## 56      PROF =~  Im1  4.223 -0.192  -0.177   -0.133   -0.133
## 57      Im20 ~~  Im6  4.215 -0.064  -0.064   -0.115   -0.115
## 58  PRODQUAL =~  Im1  4.027  0.145   0.102    0.077    0.077
## 59  PRODQUAL =~  Im2  4.027 -0.129  -0.090   -0.070   -0.070
## 60      PROF =~ Im12  3.965 -0.117  -0.108   -0.095   -0.095
## 61      Im14 ~~  Im6  3.823  0.027   0.027    0.149    0.149
## 62      FOOD =~  Im6  3.804 -0.271  -0.220   -0.183   -0.183
## 63      FOOD =~  Im7  3.804  0.321   0.260    0.215    0.215
## 64       Im2 ~~ Im17  3.691  0.033   0.033    0.192    0.192
## 65       Im4 ~~  Im6  3.588  0.033   0.033    0.143    0.143
## 66       Im3 ~~ Im17  3.342  0.028   0.028    0.198    0.198
## 67      Im11 ~~  Im1  3.335 -0.045  -0.045   -0.189   -0.189
## 68       Im5 ~~  Im1  3.275  0.043   0.043    0.188    0.188
## 69      PROF =~ Im20  3.209 -0.113  -0.104   -0.069   -0.069
## 70    CHOICE =~ Im21  3.202  0.067   0.087    0.064    0.064
## 71       Im3 ~~  Im2  3.151  0.026   0.026    0.100    0.100
## 72      Im20 ~~ Im13  3.089  0.055   0.055    0.111    0.111
## 73      Im18 ~~  Im6  3.067  0.046   0.046    0.091    0.091
## 74      Im14 ~~  Im7  3.014 -0.026  -0.026   -0.272   -0.272
## 75      Im11 ~~ Im17  2.983 -0.045  -0.045   -0.163   -0.163
## 76    FRENCH =~ Im11  2.967  0.080   0.078    0.069    0.069
## 77     ATMOS =~ Im13  2.904  0.062   0.078    0.065    0.065
## 78       Im5 ~~  Im7  2.807  0.048   0.048    0.154    0.154
## 79      Im10 ~~ Im11  2.784  0.028   0.028    0.093    0.093
## 80      Im20 ~~  Im1  2.774 -0.042  -0.042   -0.198   -0.198
## 81       Im5 ~~ Im14  2.721  0.026   0.026    0.115    0.115
## 82       Im1 ~~ Im17  2.656 -0.029  -0.029   -0.359   -0.359
## 83    FRENCH =~ Im19  2.578  0.085   0.083    0.074    0.074
## 84    FRENCH =~ Im16  2.578 -0.082  -0.080   -0.066   -0.066
## 85       Im2 ~~ Im16  2.577  0.038   0.038    0.088    0.088
## 86    CHOICE =~ Im14  2.577  0.027   0.035    0.041    0.041
## 87    CHOICE =~ Im10  2.577 -0.026  -0.035   -0.039   -0.039
## 88      Im21 ~~ Im18  2.573 -0.052  -0.052   -0.084   -0.084
## 89       Im4 ~~ Im11  2.457 -0.034  -0.034   -0.113   -0.113
## 90      PROF =~ Im13  2.455  0.096   0.089    0.074    0.074
## 91      Im22 ~~ Im19  2.419 -0.049  -0.049   -0.115   -0.115
## 92       Im4 ~~ Im22  2.418 -0.034  -0.034   -0.138   -0.138
## 93       Im3 ~~ Im20  2.350 -0.034  -0.034   -0.093   -0.093
## 94      Im12 ~~  Im7  2.333  0.036   0.036    0.178    0.178
## 95      DECO =~ Im12  2.244 -0.054  -0.066   -0.058   -0.058
## 96      Im11 ~~  Im7  2.221  0.044   0.044    0.137    0.137
## 97      Im19 ~~ Im17  2.187  0.035   0.035    0.193    0.193
## 98  PRODQUAL =~ Im16  2.157 -0.133  -0.094   -0.078   -0.078
## 99  PRODQUAL =~ Im19  2.157  0.140   0.098    0.087    0.087
## 100     Im10 ~~ Im17  2.035 -0.017  -0.017   -0.161   -0.161
## 101     Im14 ~~ Im17  1.988  0.016   0.016    0.201    0.201
## 102      Im4 ~~  Im1  1.978  0.020   0.020    0.227    0.227
## 103      Im3 ~~ Im12  1.906 -0.024  -0.024   -0.092   -0.092
## 104     Im12 ~~  Im6  1.902 -0.033  -0.033   -0.084   -0.084
## 105   CHOICE =~ Im16  1.817  0.068   0.089    0.074    0.074
## 106   CHOICE =~ Im19  1.817 -0.071  -0.093   -0.083   -0.083
## 107     Im14 ~~  Im2  1.800  0.015   0.015    0.098    0.098
## 108     Im18 ~~  Im7  1.743 -0.033  -0.033   -0.128   -0.128
## 109   FRENCH =~  Im5  1.735  0.059   0.057    0.043    0.043
## 110     Im11 ~~  Im2  1.713  0.033   0.033    0.064    0.064
## 111    ATMOS =~ Im17  1.684 -0.057  -0.073   -0.058   -0.058
## 112    ATMOS =~ Im18  1.684  0.057   0.072    0.052    0.052
## 113     Im19 ~~ Im18  1.680 -0.034  -0.034   -0.082   -0.082
## 114    BRAND =~  Im3  1.663  0.034   0.041    0.031    0.031
## 115      Im3 ~~ Im14  1.662 -0.012  -0.012   -0.102   -0.102
## 116   FRENCH =~  Im2  1.647  0.039   0.038    0.030    0.030
## 117   FRENCH =~  Im1  1.647 -0.045  -0.043   -0.033   -0.033
## 118     Im22 ~~  Im2  1.646 -0.032  -0.032   -0.077   -0.077
## 119     Im22 ~~ Im18  1.613  0.041   0.041    0.077    0.077
## 120     FOOD =~  Im2  1.604  0.050   0.040    0.031    0.031
## 121     FOOD =~  Im1  1.604 -0.056  -0.046   -0.034   -0.034
## 122 PRODQUAL =~  Im4  1.602 -0.058  -0.041   -0.030   -0.030
## 123     Im22 ~~ Im13  1.588 -0.040  -0.040   -0.086   -0.086
## 124      Im4 ~~  Im2  1.557 -0.018  -0.018   -0.095   -0.095
## 125     Im14 ~~ Im21  1.552  0.021   0.021    0.091    0.091
## 126      Im5 ~~ Im16  1.529 -0.043  -0.043   -0.064   -0.064
## 127     Im12 ~~ Im17  1.526 -0.026  -0.026   -0.151   -0.151
## 128     Im10 ~~ Im18  1.519  0.018   0.018    0.072    0.072
## 129 PRODQUAL =~ Im22  1.519 -0.095  -0.067   -0.044   -0.044
## 130      Im2 ~~ Im18  1.481 -0.026  -0.026   -0.063   -0.063
## 131     Im12 ~~ Im13  1.475  0.089   0.089    0.257    0.257
## 132 PRODQUAL =~  Im6  1.473 -0.073  -0.052   -0.043   -0.043
## 133 PRODQUAL =~  Im7  1.473  0.087   0.061    0.051    0.051
## 134     Im14 ~~ Im18  1.464 -0.017  -0.017   -0.088   -0.088
## 135     PROF =~ Im22  1.445  0.077   0.071    0.047    0.047
## 136     DECO =~ Im13  1.431  0.045   0.055    0.046    0.046
## 137 PRODQUAL =~ Im17  1.422  0.109   0.076    0.062    0.062
## 138 PRODQUAL =~ Im18  1.422 -0.108  -0.076   -0.054   -0.054
## 139      Im4 ~~ Im12  1.373  0.019   0.019    0.106    0.106
## 140    ATMOS =~  Im1  1.355  0.043   0.054    0.040    0.040
## 141    ATMOS =~  Im2  1.355 -0.038  -0.048   -0.037   -0.037
## 142     Im22 ~~  Im7  1.342  0.035   0.035    0.133    0.133
## 143      Im3 ~~ Im18  1.316 -0.022  -0.022   -0.065   -0.065
## 144      Im3 ~~ Im11  1.290  0.025   0.025    0.061    0.061
## 145     PROF =~  Im4  1.267 -0.055  -0.050   -0.037   -0.037
## 146     Im13 ~~ Im19  1.244  0.029   0.029    0.080    0.080
## 147      Im3 ~~ Im10  1.231  0.011   0.011    0.071    0.071
## 148     Im10 ~~ Im12  1.205  0.014   0.014    0.077    0.077
## 149     Im12 ~~ Im16  1.199  0.030   0.030    0.071    0.071
## 150    BRAND =~ Im11  1.070 -0.047  -0.056   -0.049   -0.049
## 151    BRAND =~  Im2  1.067  0.042   0.051    0.039    0.039
## 152    BRAND =~  Im1  1.067 -0.048  -0.057   -0.043   -0.043
## 153     Im14 ~~ Im12  1.061 -0.013  -0.013   -0.090   -0.090
## 154      Im4 ~~  Im7  1.054 -0.017  -0.017   -0.147   -0.147
## 155 PRODQUAL =~ Im20  1.037  0.077   0.054    0.036    0.036
## 156     Im21 ~~ Im17  1.017  0.027   0.027    0.101    0.101
## 157     Im20 ~~ Im19  0.988  0.031   0.031    0.068    0.068
## 158     PROF =~ Im17  0.986  0.084   0.077    0.062    0.062
## 159     PROF =~ Im18  0.986 -0.083  -0.077   -0.055   -0.055
## 160     Im19 ~~  Im7  0.949  0.025   0.025    0.122    0.122
## 161     PROF =~  Im7  0.940 -0.060  -0.055   -0.045   -0.045
## 162     PROF =~  Im6  0.940  0.050   0.046    0.039    0.039
## 163     Im13 ~~ Im18  0.925 -0.026  -0.026   -0.057   -0.057
## 164      Im5 ~~  Im2  0.918 -0.023  -0.023   -0.047   -0.047
## 165     Im14 ~~ Im13  0.889  0.013   0.013    0.079    0.079
## 166     Im16 ~~  Im7  0.880 -0.027  -0.027   -0.097   -0.097
## 167      Im1 ~~ Im18  0.847  0.019   0.019    0.101    0.101
## 168    ATMOS =~  Im3  0.826  0.022   0.028    0.022    0.022
## 169     FOOD =~ Im20  0.814 -0.052  -0.042   -0.028   -0.028
## 170     Im22 ~~  Im6  0.806  0.028   0.028    0.054    0.054
## 171      Im5 ~~ Im19  0.786 -0.026  -0.026   -0.052   -0.052
## 172    BRAND =~ Im16  0.775 -0.050  -0.060   -0.050   -0.050
## 173    BRAND =~ Im19  0.775  0.052   0.063    0.056    0.056
## 174      Im3 ~~ Im19  0.774  0.016   0.016    0.061    0.061
## 175    BRAND =~ Im14  0.773  0.017   0.020    0.023    0.023
## 176    BRAND =~ Im10  0.773 -0.016  -0.020   -0.022   -0.022
## 177     Im10 ~~ Im19  0.726 -0.012  -0.012   -0.062   -0.062
## 178   FRENCH =~ Im13  0.706 -0.035  -0.034   -0.028   -0.028
## 179     PROF =~  Im5  0.688  0.055   0.051    0.038    0.038
## 180      Im4 ~~  Im5  0.687  0.029   0.029    0.103    0.103
## 181     Im20 ~~ Im12  0.675  0.024   0.024    0.054    0.054
## 182      Im2 ~~  Im7  0.669  0.016   0.016    0.079    0.079
## 183      Im3 ~~  Im7  0.637 -0.014  -0.014   -0.084   -0.084
## 184 PRODQUAL =~ Im14  0.619  0.031   0.022    0.025    0.025
## 185 PRODQUAL =~ Im10  0.619 -0.030  -0.021   -0.024   -0.024
## 186     Im21 ~~  Im7  0.611 -0.023  -0.023   -0.076   -0.076
## 187      Im5 ~~ Im22  0.596  0.028   0.028    0.044    0.044
## 188      Im4 ~~ Im10  0.595 -0.007  -0.007   -0.066   -0.066
## 189     Im20 ~~ Im18  0.582  0.025   0.025    0.043    0.043
## 190     Im10 ~~  Im2  0.581 -0.008  -0.008   -0.045   -0.045
## 191      Im4 ~~ Im16  0.579  0.016   0.016    0.062    0.062
## 192     Im21 ~~  Im2  0.574  0.019   0.019    0.039    0.039
## 193     Im10 ~~ Im21  0.544 -0.013  -0.013   -0.043   -0.043
## 194     Im14 ~~ Im22  0.525 -0.012  -0.012   -0.062   -0.062
## 195     Im13 ~~  Im7  0.518 -0.018  -0.018   -0.080   -0.080
## 196      Im5 ~~ Im11  0.501  0.026   0.026    0.033    0.033
## 197     Im20 ~~ Im11  0.498  0.027   0.027    0.038    0.038
## 198     Im12 ~~  Im2  0.492 -0.013  -0.013   -0.043   -0.043
## 199     Im11 ~~ Im18  0.492  0.023   0.023    0.035    0.035
## 200   CHOICE =~  Im3  0.483 -0.015  -0.020   -0.015   -0.015
## 201      Im1 ~~ Im16  0.483 -0.017  -0.017   -0.082   -0.082
## 202     Im21 ~~ Im12  0.479  0.020   0.020    0.043    0.043
## 203      Im5 ~~ Im10  0.474 -0.011  -0.011   -0.039   -0.039
## 204   CHOICE =~ Im11  0.473 -0.026  -0.034   -0.030   -0.030
## 205     Im10 ~~ Im20  0.466  0.012   0.012    0.043    0.043
## 206     PROF =~  Im3  0.453  0.032   0.029    0.022    0.022
## 207   FRENCH =~  Im3  0.431 -0.019  -0.018   -0.014   -0.014
## 208     FOOD =~  Im3  0.430 -0.023  -0.019   -0.014   -0.014
## 209     FOOD =~ Im19  0.429  0.047   0.038    0.034    0.034
## 210     FOOD =~ Im16  0.429 -0.045  -0.037   -0.031   -0.031
## 211     PROF =~ Im11  0.410  0.039   0.036    0.032    0.032
## 212      Im5 ~~ Im20  0.382  0.023   0.023    0.033    0.033
## 213     Im13 ~~  Im6  0.377  0.016   0.016    0.036    0.036
## 214     Im14 ~~ Im19  0.372  0.009   0.009    0.056    0.056
## 215     Im21 ~~ Im13  0.372 -0.019  -0.019   -0.036   -0.036
## 216     PROF =~ Im21  0.371  0.036   0.033    0.024    0.024
## 217   CHOICE =~  Im4  0.369 -0.014  -0.018   -0.013   -0.013
## 218     Im22 ~~ Im17  0.360  0.016   0.016    0.071    0.071
## 219   FRENCH =~ Im21  0.360 -0.029  -0.028   -0.020   -0.020
## 220     Im21 ~~ Im11  0.346 -0.022  -0.022   -0.029   -0.029
## 221      Im5 ~~ Im17  0.345  0.015   0.015    0.055    0.055
## 222     Im14 ~~ Im20  0.330 -0.010  -0.010   -0.045   -0.045
## 223     FOOD =~ Im21  0.320  0.032   0.026    0.019    0.019
## 224   CHOICE =~ Im17  0.309  0.023   0.030    0.024    0.024
## 225   CHOICE =~ Im18  0.309 -0.023  -0.030   -0.021   -0.021
## 226      Im3 ~~ Im13  0.299  0.010   0.010    0.035    0.035
## 227      Im4 ~~ Im19  0.281 -0.010  -0.010   -0.050   -0.050
## 228     Im22 ~~ Im16  0.277  0.019   0.019    0.033    0.033
## 229      Im5 ~~ Im21  0.277 -0.019  -0.019   -0.026   -0.026
## 230      Im4 ~~ Im14  0.246  0.005   0.005    0.053    0.053
## 231     DECO =~ Im11  0.238  0.019   0.024    0.021    0.021
## 232     Im16 ~~ Im18  0.231 -0.015  -0.015   -0.026   -0.026
## 233     Im17 ~~  Im7  0.228 -0.010  -0.010   -0.094   -0.094
## 234     Im21 ~~ Im16  0.227 -0.017  -0.017   -0.026   -0.026
## 235     Im20 ~~ Im22  0.211  0.043   0.043    0.074    0.074
## 236     Im17 ~~  Im6  0.208  0.010   0.010    0.045    0.045
## 237     Im20 ~~  Im2  0.203 -0.011  -0.011   -0.025   -0.025
## 238      Im2 ~~ Im19  0.202 -0.009  -0.009   -0.029   -0.029
## 239     FOOD =~  Im4  0.194 -0.016  -0.013   -0.010   -0.010
## 240      Im4 ~~ Im13  0.168 -0.007  -0.007   -0.035   -0.035
## 241     Im14 ~~ Im11  0.165  0.007   0.007    0.028    0.028
## 242     FOOD =~ Im22  0.151  0.023   0.018    0.012    0.012
## 243     Im12 ~~ Im18  0.146 -0.010  -0.010   -0.024   -0.024
## 244     Im20 ~~ Im16  0.145  0.014   0.014    0.022    0.022
## 245     Im21 ~~  Im1  0.132  0.009   0.009    0.040    0.040
## 246    ATMOS =~ Im19  0.131 -0.017  -0.022   -0.019   -0.019
## 247    ATMOS =~ Im16  0.131  0.016   0.021    0.017    0.017
## 248      Im4 ~~ Im20  0.129  0.008   0.008    0.029    0.029
## 249      Im1 ~~  Im7  0.126 -0.007  -0.007   -0.075   -0.075
## 250     Im12 ~~  Im1  0.110 -0.006  -0.006   -0.044   -0.044
## 251      Im3 ~~  Im6  0.106  0.006   0.006    0.018    0.018
## 252      Im2 ~~  Im6  0.094 -0.006  -0.006   -0.016   -0.016
## 253   FRENCH =~ Im18  0.094  0.013   0.012    0.009    0.009
## 254   FRENCH =~ Im17  0.094 -0.013  -0.013   -0.010   -0.010
## 255     Im10 ~~  Im1  0.093 -0.003  -0.003   -0.038   -0.038
## 256 PRODQUAL =~ Im21  0.088  0.021   0.015    0.011    0.011
## 257      Im5 ~~ Im18  0.083  0.009   0.009    0.014    0.014
## 258     Im20 ~~  Im7  0.082  0.009   0.009    0.030    0.030
## 259     DECO =~  Im2  0.075  0.009   0.011    0.008    0.008
## 260     DECO =~  Im1  0.075 -0.010  -0.012   -0.009   -0.009
## 261      Im5 ~~ Im12  0.067  0.007   0.007    0.015    0.015
## 262     Im14 ~~  Im1  0.063 -0.003  -0.003   -0.039   -0.039
## 263    ATMOS =~ Im14  0.061  0.004   0.006    0.006    0.006
## 264    ATMOS =~ Im10  0.061 -0.004  -0.006   -0.006   -0.006
## 265     Im21 ~~ Im19  0.060  0.008   0.008    0.015    0.015
## 266      Im4 ~~ Im21  0.059  0.005   0.005    0.018    0.018
## 267     PROF =~ Im10  0.058  0.008   0.007    0.008    0.008
## 268     PROF =~ Im14  0.058 -0.008  -0.007   -0.009   -0.009
## 269      Im1 ~~ Im19  0.056 -0.005  -0.005   -0.034   -0.034
## 270   CHOICE =~  Im6  0.055 -0.007  -0.009   -0.007   -0.007
## 271   CHOICE =~  Im7  0.055  0.008   0.010    0.008    0.008
## 272     DECO =~ Im14  0.052  0.005   0.006    0.007    0.007
## 273     DECO =~ Im10  0.052 -0.005  -0.006   -0.006   -0.006
## 274     Im10 ~~ Im22  0.051  0.004   0.004    0.015    0.015
## 275   FRENCH =~ Im12  0.045 -0.008  -0.008   -0.007   -0.007
## 276      Im1 ~~  Im6  0.039 -0.004  -0.004   -0.021   -0.021
## 277    ATMOS =~  Im6  0.036 -0.006  -0.008   -0.007   -0.007
## 278    ATMOS =~  Im7  0.036  0.008   0.010    0.008    0.008
## 279     Im12 ~~ Im19  0.023 -0.004  -0.004   -0.011   -0.011
## 280     DECO =~ Im21  0.016  0.005   0.006    0.005    0.005
## 281     FOOD =~ Im17  0.015  0.006   0.005    0.004    0.004
## 282     FOOD =~ Im18  0.015 -0.006  -0.005   -0.004   -0.004
## 283      Im3 ~~ Im21  0.013 -0.003  -0.003   -0.006   -0.006
## 284     Im16 ~~  Im6  0.011 -0.003  -0.003   -0.006   -0.006
## 285     Im19 ~~  Im6  0.009 -0.002  -0.002   -0.006   -0.006
## 286     Im11 ~~ Im19  0.006 -0.002  -0.002   -0.005   -0.005
## 287     Im21 ~~  Im6  0.006  0.002   0.002    0.004    0.004
## 288     DECO =~ Im16  0.004  0.004   0.005    0.004    0.004
## 289     DECO =~ Im19  0.004 -0.004  -0.005   -0.004   -0.004
## 290     Im11 ~~ Im16  0.002  0.002   0.002    0.002    0.002
## 291   FRENCH =~ Im14  0.001  0.001   0.001    0.002    0.002
## 292   FRENCH =~ Im10  0.001 -0.001  -0.001   -0.002   -0.002
## 293      Im3 ~~ Im16  0.001 -0.001  -0.001   -0.002   -0.002
## 294   FRENCH =~  Im4  0.001 -0.001  -0.001    0.000    0.000
## 295     Im16 ~~ Im17  0.000  0.000   0.000    0.002    0.002
## 296 PRODQUAL =~  Im3  0.000  0.000   0.000    0.000    0.000
## 297      Im5 ~~ Im13  0.000  0.000   0.000    0.000    0.000
## 298    BRAND =~ Im21  0.000  0.000   0.000    0.000    0.000
## 299     FOOD =~ Im12  0.000  0.000   0.000    0.000    0.000

2.4 SEM

## don't actually think we need this as we can use the full data for confirmatory and path analysis
# data_img_EFA2
# data.frame(EFA_PAFn[[3]]$scores)
# 
# numcol_data_img_EFA = dim(data_img_EFA2)[2]
# numcol_scores = dim(EFA_PAFn[[3]]$scores)[2]
# numcol_data_img_EFA
# numcol_scores
# 
# CFA_data = cbind(data_img_EFA2, EFA_PAFn[[3]]$scores, survey_excl_img2["SAT_1"])
# CFA_data
# # colnames(CFA_data)[23:29] = c("Gourmet food", "Brand image", "Choice range", "Relaxed atmosphere", "Decoration", "Product quality", "Frenchness")
# 
# # colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO")
# colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO", "QUAL", "FRENCH")
# 
# CFA_data

2.4.1 model images to mediators

# missing Im8, Im15, Im9

# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2  
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "

# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7

AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4

SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH
"

2.4.2 linear regression

# # linear regression
# lm_SAT_1 <-  lm (model_SAT_1, data = survey) 
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.3 path analysis

# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 143 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       148
## 
##   Number of observations                           553
##   Number of missing patterns                       135
## 
## Model Test User Model:
##                                                       
##   Test statistic                               807.817
##   Degrees of freedom                               412
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             11978.557
##   Degrees of freedom                               496
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.966
##   Tucker-Lewis Index (TLI)                       0.959
##                                                       
##   Robust Comparative Fit Index (CFI)             0.966
##   Robust Tucker-Lewis Index (TLI)                0.959
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -22422.581
##   Loglikelihood unrestricted model (H1)     -22018.673
##                                                       
##   Akaike (AIC)                               45141.162
##   Bayesian (BIC)                             45779.835
##   Sample-size adjusted Bayesian (SABIC)      45310.018
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.042
##   90 Percent confidence interval - lower         0.037
##   90 Percent confidence interval - upper         0.046
##   P-value H_0: RMSEA <= 0.050                    0.999
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   0.042
##   90 Percent confidence interval - lower         0.038
##   90 Percent confidence interval - upper         0.047
##   P-value H_0: Robust RMSEA <= 0.050             0.998
##   P-value H_0: Robust RMSEA >= 0.080             0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.059
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.235    0.936
##     Im4               1.057    0.025   42.676    0.000    1.306    0.970
##     Im5               0.818    0.034   23.801    0.000    1.010    0.760
##   FOOD =~                                                               
##     Im10              1.000                               0.810    0.921
##     Im14              1.019    0.036   28.596    0.000    0.826    0.954
##   ATMOS =~                                                              
##     Im20              1.000                               1.253    0.838
##     Im21              0.865    0.041   20.940    0.000    1.084    0.791
##     Im22              1.060    0.046   23.188    0.000    1.327    0.869
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.703    0.615
##     Im12              1.409    0.094   15.045    0.000    0.991    0.872
##     Im13              1.464    0.105   13.957    0.000    1.029    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.302    0.978
##     Im2               0.889    0.032   27.907    0.000    1.157    0.900
##   PROF =~                                                               
##     Im16              1.000                               0.911    0.757
##     Im19              1.030    0.056   18.278    0.000    0.938    0.834
##   BRAND =~                                                              
##     Im17              1.000                               1.205    0.970
##     Im18              0.992    0.041   24.147    0.000    1.196    0.856
##   FRENCH =~                                                             
##     Im6               1.000                               0.986    0.822
##     Im7               1.161    0.066   17.619    0.000    1.144    0.945
##   AFCOM =~                                                              
##     COM_A1            1.000                               1.120    0.785
##     COM_A2            1.180    0.056   21.211    0.000    1.321    0.830
##     COM_A3            1.176    0.059   19.829    0.000    1.317    0.816
##     COM_A4            1.297    0.063   20.613    0.000    1.453    0.845
##   SAT =~                                                                
##     SAT_1             1.000                               0.868    0.859
##     SAT_2             0.937    0.049   19.036    0.000    0.814    0.818
##     SAT_3             0.812    0.055   14.799    0.000    0.705    0.620
##   RI =~                                                                 
##     C_REP1            1.000                               0.588    0.798
##     C_REP2            1.021    0.047   21.905    0.000    0.601    0.955
##     C_REP3            0.719    0.038   19.135    0.000    0.423    0.758
##   COI =~                                                                
##     C_CR1             1.000                               1.641    0.848
##     C_CR3             1.033    0.051   20.134    0.000    1.695    0.822
##     C_CR4             0.967    0.049   19.687    0.000    1.587    0.805
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   SAT ~                                                                 
##     DECO             -0.107    0.046   -2.357    0.018   -0.153   -0.153
##     CHOICE            0.095    0.040    2.379    0.017    0.142    0.142
##     PROF              0.615    0.090    6.808    0.000    0.645    0.645
##   AFCOM ~                                                               
##     ATMOS             0.437    0.047    9.282    0.000    0.489    0.489
##     PRODQUAL         -0.037    0.076   -0.485    0.628   -0.023   -0.023
##     FRENCH            0.206    0.051    4.031    0.000    0.182    0.182
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.416    0.050    8.380    0.000    0.416    0.416
##     ATMOS             0.730    0.081    8.972    0.000    0.472    0.472
##     PRODQUAL          0.408    0.051    8.031    0.000    0.470    0.470
##     CHOICE            0.709    0.079    9.024    0.000    0.441    0.441
##     PROF              0.750    0.070   10.690    0.000    0.667    0.667
##     BRAND             0.768    0.076   10.124    0.000    0.516    0.516
##     FRENCH            0.412    0.063    6.494    0.000    0.338    0.338
##     RI                0.181    0.035    5.193    0.000    0.249    0.249
##     COI               0.047    0.095    0.492    0.623    0.023    0.023
##   FOOD ~~                                                               
##     ATMOS             0.303    0.050    6.019    0.000    0.299    0.299
##     PRODQUAL          0.257    0.034    7.652    0.000    0.452    0.452
##     CHOICE            0.328    0.050    6.606    0.000    0.311    0.311
##     PROF              0.387    0.043    8.999    0.000    0.525    0.525
##     BRAND             0.317    0.047    6.798    0.000    0.325    0.325
##     FRENCH            0.469    0.047   10.016    0.000    0.588    0.588
##     RI                0.123    0.023    5.283    0.000    0.258    0.258
##     COI              -0.044    0.063   -0.700    0.484   -0.033   -0.033
##   ATMOS ~~                                                              
##     PRODQUAL          0.370    0.053    7.026    0.000    0.420    0.420
##     CHOICE            0.748    0.084    8.879    0.000    0.458    0.458
##     PROF              0.580    0.068    8.542    0.000    0.508    0.508
##     BRAND             0.785    0.080    9.748    0.000    0.520    0.520
##     FRENCH            0.411    0.065    6.374    0.000    0.333    0.333
##     RI                0.281    0.040    7.034    0.000    0.381    0.381
##     COI               0.436    0.103    4.210    0.000    0.212    0.212
##   PRODQUAL ~~                                                           
##     CHOICE            0.437    0.054    8.146    0.000    0.477    0.477
##     PROF              0.348    0.043    8.092    0.000    0.543    0.543
##     BRAND             0.479    0.053    9.046    0.000    0.566    0.566
##     FRENCH            0.211    0.038    5.621    0.000    0.305    0.305
##     RI                0.112    0.022    5.128    0.000    0.270    0.270
##     COI               0.060    0.058    1.036    0.300    0.052    0.052
##   CHOICE ~~                                                             
##     PROF              0.725    0.071   10.200    0.000    0.611    0.611
##     BRAND             0.816    0.079   10.366    0.000    0.520    0.520
##     FRENCH            0.296    0.061    4.829    0.000    0.231    0.231
##     RI                0.216    0.037    5.829    0.000    0.282    0.282
##     COI               0.068    0.100    0.678    0.498    0.032    0.032
##   PROF ~~                                                               
##     BRAND             0.676    0.065   10.326    0.000    0.616    0.616
##     FRENCH            0.363    0.052    6.990    0.000    0.404    0.404
##     RI                0.200    0.030    6.678    0.000    0.373    0.373
##     COI              -0.079    0.077   -1.029    0.304   -0.053   -0.053
##   BRAND ~~                                                              
##     FRENCH            0.388    0.061    6.333    0.000    0.327    0.327
##     RI                0.188    0.034    5.501    0.000    0.265    0.265
##     COI               0.111    0.094    1.190    0.234    0.056    0.056
##   FRENCH ~~                                                             
##     RI                0.134    0.029    4.535    0.000    0.230    0.230
##     COI               0.004    0.078    0.051    0.959    0.002    0.002
##   RI ~~                                                                 
##     COI               0.078    0.047    1.677    0.094    0.081    0.081
##  .AFCOM ~~                                                              
##    .SAT               0.218    0.037    5.825    0.000    0.357    0.357
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.995    0.056   88.576    0.000    4.995    3.787
##    .Im4               4.999    0.057   86.999    0.000    4.999    3.713
##    .Im5               5.036    0.057   87.853    0.000    5.036    3.787
##    .Im10              6.100    0.037  162.781    0.000    6.100    6.936
##    .Im14              6.138    0.037  165.851    0.000    6.138    7.093
##    .Im20              4.672    0.064   73.228    0.000    4.672    3.125
##    .Im21              5.139    0.058   87.975    0.000    5.139    3.750
##    .Im22              4.280    0.065   65.485    0.000    4.280    2.802
##    .Im11              5.654    0.049  115.283    0.000    5.654    4.943
##    .Im12              5.666    0.049  116.116    0.000    5.666    4.985
##    .Im13              5.448    0.052  105.654    0.000    5.448    4.526
##    .Im1               4.792    0.057   84.287    0.000    4.792    3.600
##    .Im2               4.858    0.055   88.415    0.000    4.858    3.781
##    .Im16              5.135    0.052   99.179    0.000    5.135    4.269
##    .Im19              5.146    0.048  107.001    0.000    5.146    4.575
##    .Im17              5.025    0.053   94.560    0.000    5.025    4.043
##    .Im18              4.595    0.060   76.466    0.000    4.595    3.288
##    .Im6               5.827    0.051  113.792    0.000    5.827    4.858
##    .Im7               5.753    0.052  110.790    0.000    5.753    4.754
##    .COM_A1            4.287    0.061   70.288    0.000    4.287    3.007
##    .COM_A2            3.887    0.068   57.199    0.000    3.887    2.443
##    .COM_A3            3.542    0.069   51.223    0.000    3.542    2.194
##    .COM_A4            3.458    0.073   47.108    0.000    3.458    2.010
##    .SAT_1             5.343    0.043  124.118    0.000    5.343    5.289
##    .SAT_2             5.483    0.042  129.018    0.000    5.483    5.510
##    .SAT_3             5.458    0.050  109.971    0.000    5.458    4.798
##    .C_REP1            4.283    0.031  136.277    0.000    4.283    5.807
##    .C_REP2            4.507    0.027  167.674    0.000    4.507    7.164
##    .C_REP3            4.676    0.024  195.449    0.000    4.676    8.380
##    .C_CR1             2.679    0.083   32.285    0.000    2.679    1.384
##    .C_CR3             3.261    0.088   37.105    0.000    3.261    1.582
##    .C_CR4             2.786    0.084   33.092    0.000    2.786    1.414
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##    .AFCOM             0.000                               0.000    0.000
##    .SAT               0.000                               0.000    0.000
##     RI                0.000                               0.000    0.000
##     COI               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.214    0.024    8.767    0.000    0.214    0.123
##    .Im4               0.108    0.024    4.461    0.000    0.108    0.059
##    .Im5               0.747    0.049   15.220    0.000    0.747    0.423
##    .Im10              0.117    0.019    6.135    0.000    0.117    0.151
##    .Im14              0.067    0.019    3.559    0.000    0.067    0.089
##    .Im20              0.666    0.059   11.280    0.000    0.666    0.298
##    .Im21              0.703    0.055   12.679    0.000    0.703    0.374
##    .Im22              0.571    0.060    9.496    0.000    0.571    0.245
##    .Im11              0.814    0.055   14.788    0.000    0.814    0.622
##    .Im12              0.310    0.040    7.841    0.000    0.310    0.240
##    .Im13              0.390    0.045    8.730    0.000    0.390    0.269
##    .Im1               0.076    0.048    1.598    0.110    0.076    0.043
##    .Im2               0.312    0.042    7.417    0.000    0.312    0.189
##    .Im16              0.618    0.051   12.116    0.000    0.618    0.427
##    .Im19              0.385    0.045    8.653    0.000    0.385    0.304
##    .Im17              0.093    0.045    2.055    0.040    0.093    0.060
##    .Im18              0.524    0.055    9.587    0.000    0.524    0.268
##    .Im6               0.468    0.054    8.714    0.000    0.468    0.325
##    .Im7               0.155    0.062    2.520    0.012    0.155    0.106
##    .COM_A1            0.779    0.060   13.036    0.000    0.779    0.383
##    .COM_A2            0.787    0.067   11.838    0.000    0.787    0.311
##    .COM_A3            0.872    0.070   12.387    0.000    0.872    0.335
##    .COM_A4            0.849    0.075   11.385    0.000    0.849    0.287
##    .SAT_1             0.267    0.034    7.920    0.000    0.267    0.262
##    .SAT_2             0.328    0.033    9.901    0.000    0.328    0.331
##    .SAT_3             0.797    0.056   14.318    0.000    0.797    0.616
##    .C_REP1            0.198    0.016   12.178    0.000    0.198    0.364
##    .C_REP2            0.035    0.011    3.224    0.001    0.035    0.089
##    .C_REP3            0.133    0.009   14.064    0.000    0.133    0.426
##    .C_CR1             1.054    0.114    9.275    0.000    1.054    0.281
##    .C_CR3             1.375    0.131   10.514    0.000    1.375    0.324
##    .C_CR4             1.366    0.123   11.130    0.000    1.366    0.352
##     DECO              1.526    0.107   14.317    0.000    1.000    1.000
##     FOOD              0.657    0.049   13.302    0.000    1.000    1.000
##     ATMOS             1.569    0.135   11.580    0.000    1.000    1.000
##     PRODQUAL          0.494    0.067    7.362    0.000    1.000    1.000
##     CHOICE            1.696    0.117   14.476    0.000    1.000    1.000
##     PROF              0.829    0.086    9.605    0.000    1.000    1.000
##     BRAND             1.452    0.104   14.014    0.000    1.000    1.000
##     FRENCH            0.971    0.094   10.349    0.000    1.000    1.000
##    .AFCOM             0.854    0.086    9.878    0.000    0.681    0.681
##    .SAT               0.436    0.050    8.755    0.000    0.579    0.579
##     RI                0.346    0.032   10.668    0.000    1.000    1.000
##     COI               2.693    0.238   11.334    0.000    1.000    1.000
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.3.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.4.3.2 local fit measures

# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.4.3.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##        DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM   SAT  RI COI
## Im3     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im4     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im5     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im10    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im14    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im20    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im21    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im22    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im11    NaN  NaN   NaN  0.378    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im12    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im13    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im1     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im2     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im16    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im19    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im17    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im18    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im6     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im7     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A4  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN 0.384 NaN NaN
## C_REP1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_REP2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_REP3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
2.4.3.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
2.4.3.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
2.4.3.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##          DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO        1                                                             
## FOOD      NaN    1                                                        
## ATMOS     NaN  NaN     1                                                  
## PRODQUAL  NaN  NaN   NaN      1                                           
## CHOICE    NaN  NaN   NaN    NaN      1                                    
## PROF      NaN  NaN   NaN    NaN    NaN    1                               
## BRAND     NaN  NaN   NaN    NaN    NaN  NaN     1                         
## FRENCH    NaN  NaN   NaN    NaN    NaN  NaN   NaN      1                  
## AFCOM     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN            
## SAT       NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN        
## RI        NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN   1    
## COI       NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN   1
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##               DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FOOD     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## ATMOS    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PRODQUAL 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## CHOICE   0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PROF     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## BRAND    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FRENCH   0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## AFCOM    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## SAT      0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## RI       0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## COI      0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
##             FRENCH     AFCOM       SAT        RI       COI
## DECO     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FOOD     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## ATMOS    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PRODQUAL 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## CHOICE   0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PROF     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## BRAND    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FRENCH   0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## AFCOM    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## SAT      0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## RI       0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## COI      0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
psi
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO      1.000                                                               
## FOOD      0.416  1.000                                                        
## ATMOS     0.472  0.299  1.000                                                 
## PRODQUAL  0.470  0.452  0.420  1.000                                          
## CHOICE    0.441  0.311  0.458  0.477  1.000                                   
## PROF      0.667  0.525  0.508  0.543  0.611  1.000                            
## BRAND     0.516  0.325  0.520  0.566  0.520  0.616  1.000                     
## FRENCH    0.338  0.588  0.333  0.305  0.231  0.404  0.327  1.000              
## AFCOM     0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.681       
## SAT       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.357  0.579
## RI        0.249  0.258  0.381  0.270  0.282  0.373  0.265  0.230  0.000  0.000
## COI       0.023 -0.033  0.212  0.052  0.032 -0.053  0.056  0.002  0.000  0.000
##              RI    COI
## DECO                  
## FOOD                  
## ATMOS                 
## PRODQUAL              
## CHOICE                
## PROF                  
## BRAND                 
## FRENCH                
## AFCOM                 
## SAT                   
## RI        1.000       
## COI       0.081  1.000
AVEpsi_fail
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO          .                                                               
## FOOD        NaN      .                                                        
## ATMOS       NaN    NaN      .                                                 
## PRODQUAL    NaN    NaN    NaN      .                                          
## CHOICE      NaN    NaN    NaN    NaN      .                                   
## PROF        NaN    NaN    NaN    NaN    NaN      .                            
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .                     
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .              
## AFCOM       NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .       
## SAT         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .
## RI          NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## COI         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
##              RI    COI
## DECO                  
## FOOD                  
## ATMOS                 
## PRODQUAL              
## CHOICE                
## PROF                  
## BRAND                 
## FRENCH                
## AFCOM                 
## SAT                   
## RI            .       
## COI         NaN      .

2.4.3.3 Modification indices

arrange(modificationindices(SEM_fit),-mi)
##          lhs op      rhs     mi    epc sepc.lv sepc.all sepc.nox
## 1      AFCOM =~   C_REP1 61.877  0.158   0.177    0.240    0.240
## 2      ATMOS ~~    AFCOM 49.054 -0.587  -0.507   -0.507   -0.507
## 3      ATMOS  ~    AFCOM 35.588 -0.540  -0.483   -0.483   -0.483
## 4      AFCOM ~~       RI 32.373  0.134   0.247    0.247    0.247
## 5     COM_A1 ~~   COM_A2 31.301  0.288   0.288    0.368    0.368
## 6      AFCOM ~~      COI 31.255  0.406   0.268    0.268    0.268
## 7      ATMOS =~   C_REP1 26.283  0.102   0.127    0.173    0.173
## 8       Im16 ~~     Im19 25.773  0.371   0.371    0.761    0.761
## 9       PROF ~~      SAT 25.773 -0.222  -0.368   -0.368   -0.368
## 10     BRAND =~     Im13 23.807  0.219   0.264    0.219    0.219
## 11    C_REP2 ~~   C_REP3 23.244  0.096   0.096    1.407    1.407
## 12       SAT ~~       RI 22.140  0.089   0.229    0.229    0.229
## 13      Im11 ~~     Im13 21.621 -0.192  -0.192   -0.341   -0.341
## 14       SAT =~   C_REP1 18.223  0.115   0.099    0.135    0.135
## 15        RI =~    SAT_2 17.895  0.232   0.137    0.137    0.137
## 16     BRAND =~     Im12 17.152 -0.178  -0.214   -0.189   -0.189
## 17    CHOICE =~     Im20 16.326 -0.160  -0.208   -0.139   -0.139
## 18        RI =~     Im22 15.906 -0.338  -0.199   -0.130   -0.130
## 19        RI =~   COM_A1 15.392  0.299   0.176    0.123    0.123
## 20      PROF  ~      SAT 14.568 -0.337  -0.322   -0.322   -0.322
## 21    CHOICE =~     Im13 14.137  0.134   0.175    0.145    0.145
## 22      Im11 ~~     Im12 13.137  0.144   0.144    0.286    0.286
## 23    COM_A3 ~~   C_REP1 13.055  0.078   0.078    0.188    0.188
## 24      FOOD =~     Im11 12.685  0.215   0.174    0.152    0.152
## 25     AFCOM =~     Im11 11.893  0.138   0.154    0.135    0.135
## 26    CHOICE =~   C_REP1 11.775  0.059   0.077    0.104    0.104
## 27       SAT  ~   FRENCH 11.592  0.143   0.163    0.163    0.163
## 28  PRODQUAL =~    C_CR4 11.365  0.307   0.216    0.109    0.109
## 29      PROF =~   COM_A3 11.354  0.198   0.180    0.112    0.112
## 30      Im21 ~~   C_REP3 11.319  0.052   0.052    0.171    0.171
## 31     ATMOS =~     Im12 11.112 -0.116  -0.146   -0.128   -0.128
## 32     AFCOM =~     Im20 10.705 -0.168  -0.188   -0.126   -0.126
## 33    FRENCH =~   C_REP1 10.658  0.075   0.074    0.100    0.100
## 34    CHOICE =~     Im12 10.534 -0.111  -0.144   -0.127   -0.127
## 35      Im21 ~~     Im22 10.334 -0.190  -0.190   -0.299   -0.299
## 36      Im13 ~~      Im1 10.251  0.066   0.066    0.382    0.382
## 37  PRODQUAL ~~    AFCOM  9.881 -0.142  -0.219   -0.219   -0.219
## 38      DECO =~   C_REP1  9.764  0.056   0.069    0.094    0.094
## 39     AFCOM  ~   CHOICE  9.453  0.130   0.151    0.151    0.151
## 40       SAT =~   COM_A2  9.449 -0.194  -0.168   -0.106   -0.106
## 41      Im13 ~~     Im17  9.292  0.068   0.068    0.358    0.358
## 42       SAT =~   COM_A3  9.262  0.199   0.173    0.107    0.107
## 43     AFCOM  ~      SAT  9.120  0.359   0.278    0.278    0.278
## 44       Im4 ~~     Im17  9.042 -0.045  -0.045   -0.453   -0.453
## 45       Im1 ~~    SAT_2  9.041 -0.055  -0.055   -0.346   -0.346
## 46  PRODQUAL  ~    AFCOM  8.849 -0.148  -0.235   -0.235   -0.235
## 47       SAT  ~    AFCOM  8.555  0.220   0.284    0.284    0.284
## 48      Im20 ~~     Im22  8.506  0.205   0.205    0.333    0.333
## 49      Im10 ~~     Im16  8.198  0.046   0.046    0.173    0.173
## 50       SAT =~     Im12  8.068 -0.129  -0.112   -0.099   -0.099
## 51     ATMOS =~     Im11  7.837  0.111   0.138    0.121    0.121
## 52     AFCOM =~     Im12  7.657 -0.091  -0.102   -0.090   -0.090
## 53      Im14 ~~     Im16  7.416 -0.043  -0.043   -0.212   -0.212
## 54      Im20 ~~     Im21  7.388  0.150   0.150    0.219    0.219
## 55  PRODQUAL =~    C_CR1  7.333 -0.237  -0.166   -0.086   -0.086
## 56    FRENCH =~     Im22  7.319  0.137   0.135    0.088    0.088
## 57       COI =~   C_REP1  7.224  0.036   0.060    0.081    0.081
## 58     ATMOS =~    C_CR4  7.213  0.140   0.176    0.089    0.089
## 59      Im10 ~~   COM_A2  7.207  0.049   0.049    0.162    0.162
## 60      DECO =~   COM_A3  7.153  0.107   0.132    0.082    0.082
## 61     BRAND =~     Im20  7.150 -0.123  -0.148   -0.099   -0.099
## 62      FOOD =~   C_REP1  7.149  0.074   0.060    0.081    0.081
## 63    CHOICE =~   C_REP3  7.114 -0.037  -0.048   -0.086   -0.086
## 64       SAT =~    C_CR4  7.053  0.194   0.169    0.086    0.086
## 65    COM_A1 ~~   COM_A4  7.039 -0.148  -0.148   -0.183   -0.183
## 66    FRENCH =~   C_REP2  7.027 -0.050  -0.050   -0.079   -0.079
## 67     ATMOS =~   C_REP3  6.995 -0.042  -0.053   -0.094   -0.094
## 68     AFCOM  ~     PROF  6.907  0.199   0.162    0.162    0.162
## 69     BRAND =~     Im22  6.898  0.122   0.148    0.097    0.097
## 70       SAT ~~      COI  6.822 -0.152  -0.140   -0.140   -0.140
## 71      Im19 ~~   C_REP1  6.618 -0.040  -0.040   -0.145   -0.145
## 72        RI =~     Im16  6.453 -0.207  -0.122   -0.101   -0.101
## 73      Im10 ~~      Im6  6.414 -0.036  -0.036   -0.152   -0.152
## 74    FRENCH =~     Im16  6.315 -0.127  -0.126   -0.104   -0.104
## 75    CHOICE =~      Im5  6.298  0.086   0.112    0.085    0.085
## 76     BRAND =~      Im4  6.287 -0.067  -0.081   -0.060   -0.060
## 77      PROF =~     Im12  6.238 -0.152  -0.138   -0.122   -0.122
## 78  PRODQUAL =~      Im5  6.228  0.173   0.121    0.091    0.091
## 79     BRAND =~    C_CR4  6.197  0.127   0.153    0.078    0.078
## 80      PROF =~   C_REP1  6.135  0.069   0.062    0.085    0.085
## 81      Im22 ~~      Im1  6.117  0.062   0.062    0.296    0.296
## 82     ATMOS =~      Im5  6.069  0.095   0.119    0.089    0.089
## 83    C_REP1 ~~   C_REP2  6.068 -0.076  -0.076   -0.909   -0.909
## 84     SAT_2 ~~    SAT_3  6.011 -0.090  -0.090   -0.177   -0.177
## 85      DECO =~    C_CR4  5.821  0.119   0.147    0.075    0.075
## 86     BRAND =~      Im5  5.807  0.096   0.115    0.087    0.087
## 87      FOOD =~      Im6  5.787 -0.269  -0.218   -0.182   -0.182
## 88     BRAND =~   COM_A3  5.704  0.099   0.120    0.074    0.074
## 89      PROF =~    C_CR4  5.642  0.168   0.153    0.078    0.078
## 90      Im13 ~~     Im16  5.612 -0.070  -0.070   -0.144   -0.144
## 91      DECO =~     Im18  5.593  0.101   0.125    0.089    0.089
## 92      DECO =~     Im17  5.593 -0.102  -0.126   -0.101   -0.101
## 93     SAT_1 ~~    SAT_3  5.570  0.092   0.092    0.200    0.200
## 94    COM_A3 ~~   COM_A4  5.532  0.152   0.152    0.176    0.176
## 95       Im3 ~~      Im1  5.490 -0.034  -0.034   -0.265   -0.265
## 96      Im10 ~~      Im7  5.466  0.034   0.034    0.252    0.252
## 97    COM_A1 ~~   C_REP2  5.455  0.034   0.034    0.207    0.207
## 98      Im22 ~~     Im12  5.408 -0.068  -0.068   -0.163   -0.163
## 99      Im11 ~~      Im6  5.400 -0.072  -0.072   -0.116   -0.116
## 100    AFCOM =~    C_CR4  5.370  0.129   0.144    0.073    0.073
## 101     Im22 ~~   C_REP2  5.355 -0.033  -0.033   -0.234   -0.234
## 102     Im16 ~~    SAT_1  5.322 -0.061  -0.061   -0.150   -0.150
## 103    ATMOS =~   C_REP2  5.286 -0.039  -0.049   -0.077   -0.077
## 104     FOOD =~   COM_A3  5.281  0.140   0.113    0.070    0.070
## 105      Im1 ~~    SAT_1  5.167  0.041   0.041    0.287    0.287
## 106     DECO =~     Im20  5.076 -0.095  -0.117   -0.079   -0.079
## 107     DECO =~   C_REP3  5.036 -0.032  -0.040   -0.072   -0.072
## 108     FOOD =~     Im13  5.010 -0.125  -0.102   -0.084   -0.084
## 109      Im5 ~~      Im6  5.010 -0.066  -0.066   -0.112   -0.112
## 110     DECO =~    C_CR1  5.008 -0.106  -0.131   -0.068   -0.068
## 111     DECO =~      Im7  4.885 -0.084  -0.104   -0.086   -0.086
## 112     PROF =~   COM_A2  4.882 -0.125  -0.114   -0.071   -0.071
## 113   CHOICE ~~    AFCOM  4.865  0.101   0.084    0.084    0.084
## 114   C_REP1 ~~   C_REP3  4.856 -0.036  -0.036   -0.225   -0.225
## 115      Im4 ~~    C_CR1  4.822 -0.064  -0.064   -0.191   -0.191
## 116      Im4 ~~     Im18  4.818  0.040   0.040    0.168    0.168
## 117     Im10 ~~     Im13  4.805 -0.031  -0.031   -0.145   -0.145
## 118     FOOD =~   C_REP2  4.798 -0.051  -0.041   -0.065   -0.065
## 119     Im13 ~~      Im2  4.787 -0.045  -0.045   -0.129   -0.129
## 120      Im3 ~~     Im22  4.764  0.049   0.049    0.139    0.139
## 121   FRENCH =~     Im20  4.724 -0.109  -0.107   -0.072   -0.072
## 122     FOOD =~      Im5  4.677  0.120   0.097    0.073    0.073
## 123     FOOD =~      Im7  4.663  0.284   0.230    0.190    0.190
## 124     Im22 ~~   C_REP3  4.654 -0.034  -0.034   -0.123   -0.123
## 125     Im20 ~~     Im17  4.627 -0.058  -0.058   -0.233   -0.233
## 126     PROF =~    SAT_2  4.584  0.130   0.118    0.119    0.119
## 127     Im22 ~~    SAT_1  4.558  0.058   0.058    0.148    0.148
## 128     PROF =~   C_REP3  4.558 -0.048  -0.043   -0.078   -0.078
## 129      Im4 ~~   COM_A3  4.540  0.051   0.051    0.168    0.168
## 130    BRAND =~    C_CR1  4.516 -0.104  -0.126   -0.065   -0.065
## 131   CHOICE  ~    AFCOM  4.498  0.114   0.098    0.098    0.098
## 132     Im11 ~~   C_REP1  4.467  0.041   0.041    0.102    0.102
## 133   COM_A1 ~~    SAT_1  4.359 -0.059  -0.059   -0.128   -0.128
## 134      COI =~   COM_A4  4.335  0.063   0.104    0.060    0.060
## 135      Im3 ~~      Im4  4.333  0.148   0.148    0.977    0.977
## 136       RI =~     Im12  4.281 -0.133  -0.078   -0.069   -0.069
## 137      Im3 ~~      Im5  4.266 -0.068  -0.068   -0.169   -0.169
## 138   FRENCH ~~      SAT  4.214  0.060   0.093    0.093    0.093
## 139      COI =~    SAT_1  4.213 -0.039  -0.064   -0.063   -0.063
## 140    BRAND =~      Im7  4.204 -0.079  -0.096   -0.079   -0.079
## 141    AFCOM =~      Im5  4.180  0.079   0.088    0.066    0.066
## 142     DECO =~      Im6  4.175  0.067   0.083    0.069    0.069
## 143       RI =~     Im21  4.151  0.163   0.096    0.070    0.070
## 144    ATMOS =~      Im4  4.122 -0.052  -0.065   -0.048   -0.048
## 145     Im14 ~~   COM_A2  4.095 -0.036  -0.036   -0.156   -0.156
## 146 PRODQUAL =~      Im2  4.068 -0.124  -0.087   -0.068   -0.068
## 147     DECO =~   COM_A2  4.009 -0.077  -0.095   -0.059   -0.059
## 148     Im20 ~~      Im6  3.960 -0.062  -0.062   -0.111   -0.111
## 149   CHOICE =~   COM_A3  3.948  0.074   0.097    0.060    0.060
## 150     PROF =~     Im13  3.914  0.126   0.114    0.095    0.095
## 151      SAT =~    C_CR1  3.891 -0.138  -0.120   -0.062   -0.062
## 152     PROF =~     Im20  3.844 -0.126  -0.115   -0.077   -0.077
## 153    BRAND =~   C_REP3  3.843 -0.029  -0.036   -0.064   -0.064
## 154     Im16 ~~   C_REP3  3.839 -0.029  -0.029   -0.102   -0.102
## 155    BRAND =~      Im6  3.805  0.065   0.079    0.066    0.066
## 156 PRODQUAL =~      Im1  3.759  0.134   0.094    0.071    0.071
## 157      Im7 ~~   C_REP2  3.754 -0.022  -0.022   -0.298   -0.298
## 158     DECO =~     Im22  3.749  0.083   0.102    0.067    0.067
## 159   COM_A4 ~~    C_CR4  3.747  0.121   0.121    0.112    0.112
## 160     FOOD =~    C_CR4  3.740  0.147   0.119    0.060    0.060
## 161      SAT  ~    ATMOS  3.739  0.072   0.104    0.104    0.104
## 162    SAT_3 ~~    C_CR3  3.717 -0.111  -0.111   -0.106   -0.106
## 163      COI =~     Im19  3.711  0.050   0.083    0.073    0.073
## 164   COM_A2 ~~    SAT_2  3.687 -0.057  -0.057   -0.113   -0.113
## 165     Im20 ~~   COM_A4  3.684  0.085   0.085    0.113    0.113
## 166     Im20 ~~     Im13  3.683  0.061   0.061    0.120    0.120
## 167      Im4 ~~      Im6  3.674  0.033   0.033    0.148    0.148
## 168     Im11 ~~      Im1  3.661 -0.047  -0.047   -0.190   -0.190
## 169     Im22 ~~    SAT_2  3.643 -0.053  -0.053   -0.121   -0.121
## 170       RI =~      Im5  3.628  0.136   0.080    0.060    0.060
## 171   COM_A1 ~~   COM_A3  3.553 -0.099  -0.099   -0.120   -0.120
## 172   COM_A2 ~~   COM_A3  3.545 -0.111  -0.111   -0.134   -0.134
## 173    SAT_1 ~~    C_CR1  3.534 -0.069  -0.069   -0.130   -0.130
## 174      Im3 ~~   COM_A4  3.528  0.048   0.048    0.112    0.112
## 175     Im22 ~~     Im11  3.500  0.071   0.071    0.105    0.105
## 176     PROF =~    C_CR1  3.432 -0.126  -0.115   -0.059   -0.059
## 177      Im2 ~~     Im17  3.429  0.032   0.032    0.188    0.188
## 178    ATMOS =~   COM_A4  3.391  0.094   0.118    0.069    0.069
## 179      Im3 ~~     Im17  3.378  0.028   0.028    0.201    0.201
## 180     Im13 ~~   C_REP2  3.372  0.022   0.022    0.185    0.185
## 181     Im22 ~~   C_REP1  3.355  0.035   0.035    0.105    0.105
## 182     PROF =~      Im2  3.355  0.161   0.147    0.114    0.114
## 183     PROF =~      Im1  3.354 -0.181  -0.165   -0.124   -0.124
## 184   C_REP2 ~~    C_CR4  3.348 -0.037  -0.037   -0.171   -0.171
## 185   FRENCH  ~      SAT  3.327  0.124   0.109    0.109    0.109
## 186     Im13 ~~   C_REP1  3.251 -0.029  -0.029   -0.103   -0.103
## 187     Im20 ~~    SAT_2  3.249  0.050   0.050    0.108    0.108
## 188     Im14 ~~      Im6  3.218  0.025   0.025    0.142    0.142
## 189      COI =~   C_REP2  3.212 -0.020  -0.033   -0.052   -0.052
## 190     Im22 ~~   COM_A1  3.204 -0.071  -0.071   -0.106   -0.106
## 191    AFCOM =~   C_REP3  3.175 -0.029  -0.033   -0.058   -0.058
## 192      COI =~     Im11  3.174  0.048   0.078    0.069    0.069
## 193     PROF =~    SAT_1  3.159 -0.113  -0.103   -0.102   -0.102
## 194      Im1 ~~   C_REP3  3.154 -0.018  -0.018   -0.179   -0.179
## 195     Im11 ~~     Im17  3.129 -0.047  -0.047   -0.169   -0.169
## 196   COM_A2 ~~    C_CR1  3.120  0.099   0.099    0.108    0.108
## 197     Im20 ~~   COM_A2  3.119 -0.074  -0.074   -0.102   -0.102
## 198     Im18 ~~      Im6  3.098  0.046   0.046    0.092    0.092
## 199     Im17 ~~   C_REP1  3.076 -0.023  -0.023   -0.172   -0.172
## 200      Im5 ~~   C_REP1  3.034  0.032   0.032    0.084    0.084
## 201   FRENCH =~     Im11  3.032  0.081   0.080    0.070    0.070
## 202 PRODQUAL =~     Im16  3.000 -0.148  -0.104   -0.087   -0.087
## 203     Im14 ~~    SAT_2  2.981  0.021   0.021    0.139    0.139
## 204 PRODQUAL =~   C_REP3  2.970 -0.046  -0.033   -0.059   -0.059
## 205     Im18 ~~   COM_A1  2.961 -0.057  -0.057   -0.090   -0.090
## 206      Im3 ~~      Im2  2.955  0.025   0.025    0.097    0.097
## 207    BRAND =~   C_REP1  2.929  0.032   0.038    0.052    0.052
## 208   COM_A1 ~~    C_CR3  2.928  0.099   0.099    0.096    0.096
## 209     Im13 ~~   COM_A2  2.909 -0.058  -0.058   -0.104   -0.104
## 210     Im14 ~~      Im7  2.900 -0.025  -0.025   -0.243   -0.243
## 211   COM_A4 ~~    SAT_1  2.891  0.053   0.053    0.111    0.111
## 212   FRENCH =~    C_CR4  2.880  0.108   0.106    0.054    0.054
## 213      Im5 ~~      Im1  2.857  0.040   0.040    0.168    0.168
## 214   FRENCH =~   COM_A3  2.841  0.090   0.089    0.055    0.055
## 215    ATMOS =~   COM_A1  2.817 -0.076  -0.095   -0.067   -0.067
## 216     Im10 ~~     Im11  2.794  0.028   0.028    0.092    0.092
## 217     Im22 ~~      Im2  2.792 -0.042  -0.042   -0.099   -0.099
## 218      SAT =~     Im19  2.751 -0.121  -0.105   -0.093   -0.093
## 219     Im10 ~~    C_CR1  2.731  0.038   0.038    0.109    0.109
## 220     Im14 ~~    C_CR1  2.727 -0.037  -0.037   -0.140   -0.140
## 221    SAT_2 ~~   C_REP1  2.724  0.023   0.023    0.090    0.090
## 222      Im5 ~~     Im14  2.721  0.026   0.026    0.117    0.117
## 223      Im2 ~~    C_CR1  2.710  0.056   0.056    0.098    0.098
## 224       RI =~     Im11  2.694  0.124   0.073    0.064    0.064
## 225      Im5 ~~      Im7  2.692  0.047   0.047    0.137    0.137
## 226   COM_A1 ~~    SAT_3  2.689  0.066   0.066    0.084    0.084
## 227      SAT =~      Im5  2.676  0.086   0.074    0.056    0.056
## 228     Im21 ~~    C_CR3  2.672 -0.091  -0.091   -0.092   -0.092
## 229      Im2 ~~    SAT_2  2.671  0.030   0.030    0.093    0.093
## 230      Im1 ~~     Im17  2.669 -0.029  -0.029   -0.347   -0.347
## 231     Im12 ~~      Im7  2.643  0.038   0.038    0.172    0.172
## 232      SAT =~     Im20  2.596 -0.092  -0.080   -0.053   -0.053
## 233     Im19 ~~    SAT_1  2.588 -0.038  -0.038   -0.117   -0.117
## 234      Im2 ~~     Im16  2.587  0.038   0.038    0.087    0.087
## 235   COM_A2 ~~    SAT_1  2.580 -0.047  -0.047   -0.103   -0.103
## 236     Im20 ~~   COM_A1  2.563 -0.064  -0.064   -0.089   -0.089
## 237   CHOICE =~     Im22  2.551  0.064   0.083    0.054    0.054
## 238    ATMOS =~    C_CR1  2.545 -0.080  -0.100   -0.052   -0.052
## 239    ATMOS =~     Im13  2.531  0.058   0.073    0.061    0.061
## 240   C_REP3 ~~    C_CR3  2.505 -0.037  -0.037   -0.086   -0.086
## 241     Im14 ~~   C_REP3  2.490  0.011   0.011    0.114    0.114
## 242    AFCOM =~    SAT_2  2.425  0.053   0.060    0.060    0.060
## 243      Im2 ~~   C_REP1  2.403  0.020   0.020    0.079    0.079
## 244      Im4 ~~     Im11  2.402 -0.033  -0.033   -0.112   -0.112
## 245      Im3 ~~    C_CR1  2.396  0.047   0.047    0.099    0.099
## 246      Im4 ~~     Im22  2.381 -0.033  -0.033   -0.134   -0.134
## 247   COM_A4 ~~    SAT_3  2.375 -0.069  -0.069   -0.083   -0.083
## 248   CHOICE =~     Im14  2.365  0.026   0.034    0.039    0.039
## 249   CHOICE =~     Im10  2.364 -0.025  -0.033   -0.038   -0.038
## 250      Im5 ~~   COM_A2  2.363  0.061   0.061    0.079    0.079
## 251     FOOD =~    C_CR1  2.363 -0.112  -0.091   -0.047   -0.047
## 252     Im22 ~~    SAT_3  2.338 -0.060  -0.060   -0.088   -0.088
## 253     Im11 ~~   C_REP2  2.334 -0.022  -0.022   -0.128   -0.128
## 254      SAT =~     Im11  2.319  0.084   0.073    0.064    0.064
## 255     FOOD =~    SAT_2  2.311  0.063   0.051    0.052    0.052
## 256     Im20 ~~      Im1  2.293 -0.038  -0.038   -0.169   -0.169
## 257   COM_A4 ~~   C_REP1  2.283  0.033   0.033    0.081    0.081
## 258 PRODQUAL =~    SAT_2  2.262  0.078   0.055    0.055    0.055
## 259   COM_A3 ~~   C_REP2  2.256 -0.024  -0.024   -0.136   -0.136
## 260   COM_A2 ~~   COM_A4  2.244 -0.096  -0.096   -0.118   -0.118
## 261      SAT =~     Im16  2.223 -0.113  -0.098   -0.081   -0.081
## 262   FRENCH =~      Im1  2.216 -0.051  -0.050   -0.038   -0.038
## 263     FOOD =~     Im16  2.214 -0.100  -0.081   -0.067   -0.067
## 264     Im21 ~~     Im18  2.214 -0.047  -0.047   -0.078   -0.078
## 265     Im13 ~~   COM_A3  2.212 -0.052  -0.052   -0.090   -0.090
## 266      SAT =~     Im13  2.196  0.072   0.062    0.052    0.052
## 267      Im2 ~~   C_REP2  2.177 -0.014  -0.014   -0.131   -0.131
## 268     Im22 ~~      Im7  2.176  0.044   0.044    0.149    0.149
## 269     Im19 ~~   COM_A1  2.173  0.047   0.047    0.086    0.086
## 270    AFCOM =~      Im2  2.170  0.041   0.045    0.035    0.035
## 271   COM_A3 ~~   C_REP3  2.156 -0.026  -0.026   -0.076   -0.076
## 272     DECO =~     Im12  2.149 -0.052  -0.065   -0.057   -0.057
## 273      Im5 ~~     Im16  2.143 -0.051  -0.051   -0.074   -0.074
## 274     Im13 ~~    SAT_2  2.137  0.033   0.033    0.092    0.092
## 275   FRENCH =~    SAT_1  2.131  0.048   0.048    0.047    0.047
## 276      Im3 ~~     Im20  2.127 -0.033  -0.033   -0.087   -0.087
## 277      COI =~      Im2  2.123  0.025   0.042    0.032    0.032
## 278      Im4 ~~      Im1  2.121  0.020   0.020    0.226    0.226
## 279      COI =~     Im13  2.103 -0.034  -0.056   -0.046   -0.046
## 280      COI =~   COM_A2  2.066  0.041   0.068    0.043    0.043
## 281      Im3 ~~   COM_A3  2.063 -0.036  -0.036   -0.084   -0.084
## 282    BRAND =~    SAT_2  2.060  0.043   0.052    0.052    0.052
## 283 PRODQUAL =~      Im6  2.054 -0.086  -0.060   -0.050   -0.050
## 284 PRODQUAL =~      Im7  2.054  0.100   0.070    0.058    0.058
## 285     Im22 ~~     Im19  2.047 -0.045  -0.045   -0.095   -0.095
## 286     Im10 ~~     Im17  2.044 -0.017  -0.017   -0.162   -0.162
## 287     Im16 ~~    C_CR4  2.028 -0.074  -0.074   -0.080   -0.080
## 288     Im22 ~~     Im18  2.023  0.046   0.046    0.084    0.084
## 289   FRENCH =~   COM_A2  2.019 -0.073  -0.072   -0.045   -0.045
## 290      Im3 ~~     Im12  2.015 -0.024  -0.024   -0.094   -0.094
## 291     Im12 ~~     Im16  2.003  0.039   0.039    0.090    0.090
## 292      Im2 ~~    SAT_1  1.991 -0.025  -0.025   -0.087   -0.087
## 293     Im12 ~~    SAT_3  1.984  0.042   0.042    0.085    0.085
## 294     Im18 ~~   C_REP1  1.983  0.023   0.023    0.071    0.071
## 295     Im19 ~~   C_REP2  1.960  0.017   0.017    0.143    0.143
## 296     Im21 ~~    C_CR4  1.960  0.076   0.076    0.077    0.077
## 297     Im14 ~~     Im17  1.948  0.016   0.016    0.206    0.206
## 298      Im2 ~~   COM_A3  1.923  0.039   0.039    0.075    0.075
## 299      SAT =~     Im18  1.917 -0.073  -0.064   -0.046   -0.046
## 300     Im14 ~~   COM_A3  1.909  0.026   0.026    0.106    0.106
## 301     Im14 ~~      Im2  1.900  0.015   0.015    0.103    0.103
## 302     FOOD =~      Im1  1.888 -0.060  -0.049   -0.037   -0.037
## 303     Im12 ~~    SAT_1  1.877 -0.028  -0.028   -0.098   -0.098
## 304    C_CR1 ~~    C_CR3  1.851  0.543   0.543    0.451    0.451
## 305     Im10 ~~   COM_A4  1.834 -0.026  -0.026   -0.083   -0.083
## 306      Im7 ~~   COM_A1  1.820 -0.041  -0.041   -0.119   -0.119
## 307     Im11 ~~      Im7  1.810  0.040   0.040    0.112    0.112
## 308     Im11 ~~   COM_A3  1.799  0.058   0.058    0.068    0.068
## 309   COM_A3 ~~    SAT_2  1.794  0.042   0.042    0.078    0.078
## 310      SAT =~      Im2  1.787  0.065   0.056    0.044    0.044
## 311    BRAND =~      Im3  1.782  0.035   0.042    0.032    0.032
## 312     Im20 ~~    SAT_1  1.779 -0.036  -0.036   -0.086   -0.086
## 313   COM_A2 ~~    SAT_3  1.771  0.056   0.056    0.071    0.071
## 314   COM_A1 ~~   C_REP3  1.769  0.022   0.022    0.067    0.067
## 315   CHOICE =~    SAT_2  1.768 -0.041  -0.054   -0.054   -0.054
## 316   CHOICE =~    C_CR4  1.742  0.062   0.080    0.041    0.041
## 317    ATMOS =~    SAT_2  1.740  0.037   0.047    0.047    0.047
## 318     PROF =~      Im4  1.737 -0.065  -0.059   -0.044   -0.044
## 319     Im10 ~~    SAT_2  1.735 -0.016  -0.016   -0.083   -0.083
## 320   FRENCH =~      Im5  1.729  0.059   0.058    0.043    0.043
## 321     Im19 ~~     Im17  1.718  0.030   0.030    0.158    0.158
## 322   FRENCH =~    C_CR1  1.715 -0.080  -0.079   -0.041   -0.041
## 323     Im20 ~~   COM_A3  1.713 -0.057  -0.057   -0.075   -0.075
## 324      Im7 ~~   COM_A2  1.692 -0.042  -0.042   -0.119   -0.119
## 325      COI =~      Im1  1.689 -0.025  -0.042   -0.031   -0.031
## 326     Im12 ~~      Im6  1.663 -0.030  -0.030   -0.080   -0.080
## 327       RI =~     Im14  1.662  0.047   0.028    0.032    0.032
## 328       RI =~     Im10  1.662 -0.046  -0.027   -0.031   -0.031
## 329     Im13 ~~   COM_A4  1.659  0.046   0.046    0.080    0.080
## 330       RI =~      Im7  1.647 -0.094  -0.055   -0.046   -0.046
## 331     Im11 ~~      Im2  1.627  0.032   0.032    0.063    0.063
## 332      COI =~     Im22  1.622 -0.037  -0.061   -0.040   -0.040
## 333      Im3 ~~     Im14  1.617 -0.012  -0.012   -0.103   -0.103
## 334   C_REP1 ~~    C_CR3  1.612  0.036   0.036    0.069    0.069
## 335      Im5 ~~    SAT_2  1.610  0.034   0.034    0.068    0.068
## 336 PRODQUAL =~      Im4  1.608 -0.058  -0.041   -0.030   -0.030
## 337       RI =~     Im19  1.585 -0.099  -0.058   -0.052   -0.052
## 338     Im12 ~~    C_CR4  1.580  0.053   0.053    0.081    0.081
## 339      COI =~      Im4  1.558 -0.020  -0.032   -0.024   -0.024
## 340      SAT =~     Im17  1.554  0.057   0.049    0.040    0.040
## 341      Im7 ~~    SAT_3  1.540  0.038   0.038    0.107    0.107
## 342     Im12 ~~     Im17  1.539 -0.026  -0.026   -0.154   -0.154
## 343     Im17 ~~   COM_A1  1.518  0.033   0.033    0.124    0.124
## 344   FRENCH =~      Im2  1.509  0.038   0.037    0.029    0.029
## 345      Im1 ~~   COM_A4  1.504 -0.034  -0.034   -0.135   -0.135
## 346     Im10 ~~     Im18  1.499  0.018   0.018    0.071    0.071
## 347      Im4 ~~      Im2  1.495 -0.017  -0.017   -0.094   -0.094
## 348       RI =~     Im13  1.495  0.082   0.048    0.040    0.040
## 349   CHOICE =~     Im21  1.486  0.046   0.060    0.043    0.043
## 350      Im2 ~~     Im18  1.484 -0.026  -0.026   -0.063   -0.063
## 351   CHOICE  ~      SAT  1.479  0.210   0.140    0.140    0.140
## 352   C_REP3 ~~    C_CR4  1.479  0.027   0.027    0.064    0.064
## 353     Im11 ~~    SAT_1  1.457  0.033   0.033    0.070    0.070
## 354     PROF =~      Im5  1.424  0.081   0.074    0.055    0.055
## 355     DECO =~     Im13  1.423  0.045   0.055    0.046    0.046
## 356     Im12 ~~     Im13  1.421  0.088   0.088    0.252    0.252
## 357     Im18 ~~   COM_A2  1.416  0.041   0.041    0.064    0.064
## 358   COM_A1 ~~    SAT_2  1.415  0.034   0.034    0.067    0.067
## 359     FOOD =~      Im2  1.413  0.046   0.038    0.029    0.029
## 360     Im12 ~~   C_REP1  1.409 -0.018  -0.018   -0.071   -0.071
## 361    AFCOM  ~     DECO  1.398  0.054   0.059    0.059    0.059
## 362     DECO ~~      SAT  1.396 -0.146  -0.179   -0.179   -0.179
## 363     Im14 ~~     Im18  1.395 -0.016  -0.016   -0.088   -0.088
## 364     Im21 ~~    SAT_3  1.392  0.045   0.045    0.061    0.061
## 365      SAT =~   COM_A1  1.385  0.070   0.061    0.043    0.043
## 366      Im1 ~~   COM_A1  1.385  0.030   0.030    0.123    0.123
## 367     Im18 ~~      Im7  1.381 -0.029  -0.029   -0.103   -0.103
## 368   COM_A3 ~~    C_CR3  1.376  0.074   0.074    0.068    0.068
## 369    SAT_2 ~~    C_CR3  1.376  0.048   0.048    0.071    0.071
## 370     Im14 ~~    C_CR4  1.375  0.028   0.028    0.092    0.092
## 371     Im10 ~~     Im12  1.375  0.015   0.015    0.081    0.081
## 372      SAT =~      Im4  1.372 -0.039  -0.034   -0.025   -0.025
## 373    AFCOM =~     Im16  1.367 -0.047  -0.053   -0.044   -0.044
## 374      Im3 ~~     Im18  1.357 -0.022  -0.022   -0.066   -0.066
## 375     Im19 ~~     Im18  1.354 -0.031  -0.031   -0.068   -0.068
## 376     Im18 ~~   C_REP3  1.351 -0.015  -0.015   -0.058   -0.058
## 377    ATMOS =~     Im17  1.348 -0.052  -0.065   -0.053   -0.053
## 378    ATMOS =~     Im18  1.348  0.052   0.065    0.046    0.046
## 379      Im4 ~~     Im12  1.347  0.019   0.019    0.105    0.105
## 380   CHOICE =~   COM_A1  1.346  0.040   0.052    0.036    0.036
## 381      Im5 ~~     Im19  1.341 -0.034  -0.034   -0.064   -0.064
## 382     Im13 ~~    SAT_3  1.338 -0.037  -0.037   -0.066   -0.066
## 383      Im3 ~~     Im11  1.307  0.026   0.026    0.061    0.061
## 384    SAT_1 ~~    C_CR4  1.304  0.044   0.044    0.073    0.073
## 385    ATMOS =~   COM_A2  1.298 -0.055  -0.069   -0.043   -0.043
## 386     Im20 ~~   C_REP2  1.295  0.016   0.016    0.108    0.108
## 387    BRAND =~     Im16  1.284 -0.059  -0.071   -0.059   -0.059
## 388    SAT_1 ~~   C_REP3  1.284  0.013   0.013    0.067    0.067
## 389      Im6 ~~      Im7  1.281  0.435   0.435    1.612    1.612
## 390   FRENCH ~~    AFCOM  1.280 -0.077  -0.085   -0.085   -0.085
## 391       RI =~   COM_A3  1.276  0.094   0.055    0.034    0.034
## 392 PRODQUAL =~     Im17  1.271  0.103   0.072    0.058    0.058
## 393 PRODQUAL =~     Im18  1.271 -0.102  -0.072   -0.051   -0.051
## 394     Im14 ~~     Im21  1.262  0.018   0.018    0.084    0.084
## 395     Im22 ~~    C_CR1  1.256 -0.058  -0.058   -0.075   -0.075
## 396     Im12 ~~   COM_A4  1.239 -0.037  -0.037   -0.072   -0.072
## 397       RI =~   COM_A4  1.230  0.093   0.055    0.032    0.032
## 398     Im20 ~~   C_REP3  1.225 -0.018  -0.018   -0.059   -0.059
## 399      Im3 ~~     Im10  1.223  0.011   0.011    0.070    0.070
## 400 PRODQUAL =~   COM_A2  1.213 -0.078  -0.055   -0.035   -0.035
## 401   FRENCH =~    SAT_3  1.209  0.051   0.050    0.044    0.044
## 402     Im10 ~~    C_CR4  1.207 -0.027  -0.027   -0.067   -0.067
## 403      Im4 ~~   COM_A4  1.202 -0.027  -0.027   -0.089   -0.089
## 404 PRODQUAL =~     Im20  1.186  0.083   0.058    0.039    0.039
## 405     PROF ~~    AFCOM  1.182  0.034   0.040    0.040    0.040
## 406   CHOICE =~    SAT_1  1.178  0.035   0.046    0.045    0.045
## 407      COI =~     Im20  1.152 -0.031  -0.051   -0.034   -0.034
## 408 PRODQUAL =~     Im22  1.149 -0.083  -0.058   -0.038   -0.038
## 409     Im10 ~~   C_REP3  1.147 -0.007  -0.007   -0.060   -0.060
## 410    SAT_1 ~~    C_CR3  1.144 -0.042  -0.042   -0.070   -0.070
## 411      COI =~    SAT_2  1.136  0.020   0.034    0.034    0.034
## 412     Im16 ~~      Im7  1.135 -0.030  -0.030   -0.098   -0.098
## 413 PRODQUAL =~     Im19  1.134  0.088   0.062    0.055    0.055
## 414      Im1 ~~   COM_A3  1.105 -0.029  -0.029   -0.113   -0.113
## 415     Im16 ~~    C_CR1  1.098  0.052   0.052    0.064    0.064
## 416      Im4 ~~      Im7  1.087 -0.018  -0.018   -0.137   -0.137
## 417     Im17 ~~   COM_A3  1.087  0.031   0.031    0.108    0.108
## 418     PROF =~      Im7  1.079 -0.065  -0.059   -0.049   -0.049
## 419    BRAND =~     Im11  1.044 -0.046  -0.055   -0.048   -0.048
## 420     PROF =~   COM_A1  1.028  0.055   0.050    0.035    0.035
## 421      Im1 ~~   COM_A2  1.000  0.027   0.027    0.108    0.108
## 422      Im6 ~~    SAT_1  0.995  0.022   0.022    0.062    0.062
## 423     Im13 ~~    C_CR3  0.995 -0.046  -0.046   -0.063   -0.063
## 424     Im14 ~~     Im12  0.989 -0.013  -0.013   -0.089   -0.089
## 425   COM_A4 ~~    C_CR3  0.982 -0.063  -0.063   -0.059   -0.059
## 426    SAT_3 ~~   C_REP3  0.980  0.016   0.016    0.049    0.049
## 427      Im1 ~~     Im18  0.980  0.021   0.021    0.104    0.104
## 428   CHOICE =~     Im16  0.965  0.048   0.063    0.052    0.052
## 429   CHOICE =~     Im19  0.965 -0.050  -0.065   -0.058   -0.058
## 430    ATMOS =~      Im2  0.957 -0.032  -0.040   -0.031   -0.031
## 431     Im16 ~~   COM_A3  0.956  0.040   0.040    0.054    0.054
## 432     Im20 ~~     Im18  0.950  0.032   0.032    0.054    0.054
## 433     Im17 ~~   COM_A4  0.902 -0.028  -0.028   -0.101   -0.101
## 434      Im5 ~~      Im2  0.897 -0.023  -0.023   -0.047   -0.047
## 435     Im13 ~~     Im18  0.892 -0.025  -0.025   -0.056   -0.056
## 436    BRAND =~    SAT_3  0.890 -0.037  -0.045   -0.040   -0.040
## 437    ATMOS =~      Im3  0.886  0.024   0.029    0.022    0.022
## 438    ATMOS =~    C_CR3  0.882 -0.050  -0.063   -0.031   -0.031
## 439   CHOICE ~~      SAT  0.882 -0.110  -0.128   -0.128   -0.128
## 440      Im1 ~~      Im2  0.880  1.034   1.034    6.695    6.695
## 441      SAT =~     Im21  0.870  0.051   0.044    0.032    0.032
## 442     Im11 ~~   COM_A2  0.868  0.038   0.038    0.048    0.048
## 443     FOOD =~     Im20  0.862 -0.054  -0.044   -0.029   -0.029
## 444     Im17 ~~   C_REP3  0.860  0.010   0.010    0.090    0.090
## 445      SAT =~      Im1  0.859 -0.049  -0.043   -0.032   -0.032
## 446    ATMOS ~~      SAT  0.859  0.034   0.041    0.041    0.041
## 447      Im7 ~~   COM_A4  0.857  0.031   0.031    0.087    0.087
## 448     Im11 ~~    C_CR4  0.857  0.051   0.051    0.048    0.048
## 449     DECO =~   C_REP2  0.849 -0.014  -0.017   -0.027   -0.027
## 450      Im6 ~~    C_CR4  0.847 -0.041  -0.041   -0.051   -0.051
## 451      Im3 ~~    SAT_1  0.845  0.015   0.015    0.061    0.061
## 452     DECO =~    SAT_2  0.832  0.026   0.033    0.033    0.033
## 453     Im19 ~~    SAT_3  0.832 -0.029  -0.029   -0.052   -0.052
## 454     Im16 ~~   COM_A4  0.828 -0.037  -0.037   -0.052   -0.052
## 455      Im6 ~~   COM_A1  0.825  0.029   0.029    0.048    0.048
## 456      Im6 ~~   C_REP2  0.824  0.010   0.010    0.081    0.081
## 457    BRAND =~      Im1  0.818 -0.039  -0.047   -0.035   -0.035
## 458      Im4 ~~    C_CR3  0.817  0.029   0.029    0.074    0.074
## 459      Im4 ~~   COM_A2  0.807 -0.021  -0.021   -0.071   -0.071
## 460      COI =~    SAT_3  0.791 -0.024  -0.040   -0.035   -0.035
## 461      Im7 ~~    C_CR4  0.785  0.038   0.038    0.082    0.082
## 462    SAT_2 ~~   C_REP3  0.783  0.010   0.010    0.048    0.048
## 463    BRAND =~   COM_A4  0.778 -0.037  -0.045   -0.026   -0.026
## 464     Im16 ~~    SAT_2  0.778  0.024   0.024    0.052    0.052
## 465     Im20 ~~     Im12  0.776  0.026   0.026    0.058    0.058
## 466     PROF =~     Im18  0.772 -0.078  -0.071   -0.051   -0.051
## 467     PROF =~     Im17  0.772  0.079   0.072    0.058    0.058
## 468     FOOD =~    SAT_3  0.770  0.050   0.040    0.036    0.036
## 469      COI =~      Im5  0.767  0.022   0.037    0.028    0.028
## 470     Im17 ~~   C_REP2  0.767  0.009   0.009    0.155    0.155
## 471      Im7 ~~    C_CR1  0.757 -0.035  -0.035   -0.087   -0.087
## 472   FRENCH =~   COM_A1  0.751 -0.042  -0.042   -0.029   -0.029
## 473   CHOICE =~   C_REP2  0.751 -0.012  -0.016   -0.026   -0.026
## 474     Im14 ~~    SAT_1  0.748 -0.010  -0.010   -0.075   -0.075
## 475     Im21 ~~     Im11  0.737 -0.032  -0.032   -0.043   -0.043
## 476      Im3 ~~     Im19  0.732  0.016   0.016    0.055    0.055
## 477     PROF =~     Im11  0.726  0.054   0.049    0.043    0.043
## 478    BRAND =~      Im2  0.725  0.033   0.039    0.031    0.031
## 479     Im12 ~~   COM_A3  0.724 -0.028  -0.028   -0.054   -0.054
## 480      Im1 ~~   C_REP2  0.720  0.008   0.008    0.154    0.154
## 481     Im14 ~~     Im13  0.716  0.012   0.012    0.072    0.072
## 482     Im20 ~~      Im2  0.715 -0.021  -0.021   -0.047   -0.047
## 483      Im2 ~~   C_REP3  0.715  0.009   0.009    0.043    0.043
## 484    BRAND =~   COM_A2  0.713 -0.034  -0.041   -0.026   -0.026
## 485      Im5 ~~    C_CR3  0.707 -0.045  -0.045   -0.045   -0.045
## 486      Im7 ~~   C_REP3  0.706  0.010   0.010    0.071    0.071
## 487      Im5 ~~    C_CR4  0.704  0.044   0.044    0.044    0.044
## 488   COM_A3 ~~    SAT_3  0.702 -0.037  -0.037   -0.044   -0.044
## 489     Im21 ~~     Im17  0.698  0.022   0.022    0.085    0.085
## 490      Im3 ~~    C_CR4  0.696 -0.027  -0.027   -0.049   -0.049
## 491     Im12 ~~   COM_A2  0.654  0.026   0.026    0.052    0.052
## 492     FOOD =~   COM_A2  0.653 -0.047  -0.038   -0.024   -0.024
## 493   COM_A4 ~~   C_REP3  0.652 -0.014  -0.014   -0.043   -0.043
## 494 PRODQUAL =~    SAT_1  0.651 -0.042  -0.029   -0.029   -0.029
## 495     Im21 ~~   C_REP1  0.650 -0.015  -0.015   -0.041   -0.041
## 496      Im4 ~~      Im5  0.638  0.028   0.028    0.099    0.099
## 497    ATMOS =~      Im1  0.638  0.029   0.036    0.027    0.027
## 498    BRAND =~     Im14  0.638  0.015   0.018    0.021    0.021
## 499    BRAND =~     Im10  0.638 -0.015  -0.018   -0.020   -0.020
## 500   FRENCH =~     Im13  0.638 -0.033  -0.033   -0.027   -0.027
## 501    AFCOM =~   C_REP2  0.636 -0.012  -0.014   -0.022   -0.022
## 502      SAT  ~ PRODQUAL  0.629  0.055   0.045    0.045    0.045
## 503 PRODQUAL =~   COM_A3  0.623  0.058   0.041    0.025    0.025
## 504      SAT =~     Im14  0.623  0.020   0.018    0.021    0.021
## 505 PRODQUAL  ~      SAT  0.621 -0.038  -0.047   -0.047   -0.047
## 506    ATMOS =~     Im19  0.620 -0.034  -0.043   -0.038   -0.038
## 507      Im4 ~~     Im10  0.613 -0.008  -0.008   -0.067   -0.067
## 508      Im2 ~~   COM_A4  0.612  0.022   0.022    0.043    0.043
## 509       RI =~      Im1  0.609 -0.046  -0.027   -0.020   -0.020
## 510     Im10 ~~      Im2  0.608 -0.009  -0.009   -0.045   -0.045
## 511     Im10 ~~   COM_A3  0.603 -0.015  -0.015   -0.046   -0.046
## 512    ATMOS =~   COM_A3  0.600  0.039   0.048    0.030    0.030
## 513     Im12 ~~    C_CR1  0.600 -0.031  -0.031   -0.054   -0.054
## 514     FOOD ~~      SAT  0.598  0.017   0.032    0.032    0.032
## 515   COM_A2 ~~    C_CR4  0.598 -0.046  -0.046   -0.044   -0.044
## 516     Im22 ~~     Im13  0.597 -0.024  -0.024   -0.051   -0.051
## 517     Im10 ~~   COM_A1  0.593 -0.014  -0.014   -0.045   -0.045
## 518       RI =~      Im4  0.589 -0.034  -0.020   -0.015   -0.015
## 519     Im21 ~~     Im12  0.585  0.022   0.022    0.047    0.047
## 520      Im7 ~~   C_REP1  0.583  0.011   0.011    0.065    0.065
## 521    SAT_3 ~~    C_CR1  0.582  0.041   0.041    0.044    0.044
## 522      Im4 ~~    C_CR4  0.581  0.024   0.024    0.061    0.061
## 523      Im7 ~~   COM_A3  0.566  0.025   0.025    0.068    0.068
## 524     Im20 ~~      Im7  0.551  0.022   0.022    0.070    0.070
## 525     Im14 ~~     Im22  0.549 -0.012  -0.012   -0.063   -0.063
## 526     Im10 ~~     Im21  0.543 -0.012  -0.012   -0.043   -0.043
## 527      Im4 ~~     Im16  0.541  0.015   0.015    0.059    0.059
## 528     PROF =~     Im22  0.532  0.048   0.043    0.028    0.028
## 529      COI =~      Im3  0.531  0.011   0.019    0.014    0.014
## 530   FRENCH =~     Im21  0.520 -0.034  -0.034   -0.025   -0.025
## 531     Im22 ~~      Im6  0.520  0.022   0.022    0.043    0.043
## 532      Im6 ~~   COM_A3  0.519 -0.025  -0.025   -0.039   -0.039
## 533      Im7 ~~    SAT_1  0.513  0.015   0.015    0.074    0.074
## 534     Im22 ~~     Im16  0.512  0.026   0.026    0.043    0.043
## 535 PRODQUAL =~   C_REP2  0.505  0.020   0.014    0.022    0.022
## 536     Im14 ~~   COM_A4  0.504  0.013   0.013    0.056    0.056
## 537     Im11 ~~     Im18  0.501  0.023   0.023    0.035    0.035
## 538      SAT =~    C_CR3  0.500 -0.053  -0.046   -0.022   -0.022
## 539     Im17 ~~    SAT_3  0.500 -0.019  -0.019   -0.070   -0.070
## 540      Im5 ~~     Im11  0.498  0.026   0.026    0.033    0.033
## 541     Im20 ~~    C_CR3  0.491 -0.040  -0.040   -0.042   -0.042
## 542      Im3 ~~      Im7  0.490 -0.012  -0.012   -0.067   -0.067
## 543     Im10 ~~     Im20  0.488  0.012   0.012    0.043    0.043
## 544   CHOICE =~    C_CR1  0.484 -0.031  -0.041   -0.021   -0.021
## 545     Im14 ~~     Im20  0.479 -0.012  -0.012   -0.055   -0.055
## 546     Im12 ~~      Im2  0.478 -0.013  -0.013   -0.043   -0.043
## 547      Im5 ~~     Im10  0.477 -0.011  -0.011   -0.038   -0.038
## 548     Im21 ~~      Im7  0.471 -0.020  -0.020   -0.061   -0.061
## 549      Im1 ~~    C_CR1  0.468 -0.023  -0.023   -0.082   -0.082
## 550     Im10 ~~    SAT_1  0.467  0.008   0.008    0.047    0.047
## 551      Im2 ~~   COM_A1  0.467 -0.018  -0.018   -0.036   -0.036
## 552 PRODQUAL =~     Im14  0.462  0.027   0.019    0.022    0.022
## 553 PRODQUAL =~     Im10  0.462 -0.026  -0.018   -0.021   -0.021
## 554      Im5 ~~     Im21  0.461 -0.025  -0.025   -0.034   -0.034
## 555     Im12 ~~    SAT_2  0.459 -0.014  -0.014   -0.045   -0.045
## 556      COI =~     Im16  0.453 -0.018  -0.030   -0.025   -0.025
## 557 PRODQUAL =~   C_REP1  0.445  0.022   0.016    0.021    0.021
## 558    BRAND =~     Im19  0.445  0.034   0.040    0.036    0.036
## 559    C_CR1 ~~    C_CR4  0.442 -0.240  -0.240   -0.200   -0.200
## 560     PROF =~      Im3  0.441  0.032   0.029    0.022    0.022
## 561   COM_A1 ~~   C_REP1  0.435 -0.013  -0.013   -0.034   -0.034
## 562    AFCOM =~     Im13  0.435 -0.023  -0.026   -0.021   -0.021
## 563    AFCOM =~    C_CR3  0.434  0.038   0.042    0.020    0.020
## 564     Im19 ~~    SAT_2  0.434  0.015   0.015    0.043    0.043
## 565   CHOICE =~      Im4  0.434 -0.015  -0.019   -0.014   -0.014
## 566     Im12 ~~   C_REP3  0.433 -0.008  -0.008   -0.039   -0.039
## 567     PROF =~      Im6  0.430  0.035   0.032    0.027    0.027
## 568      COI =~   COM_A3  0.429  0.020   0.032    0.020    0.020
## 569   CHOICE =~     Im11  0.426 -0.025  -0.032   -0.028   -0.028
## 570      Im1 ~~     Im16  0.420 -0.016  -0.016   -0.072   -0.072
## 571   CHOICE =~      Im3  0.410 -0.014  -0.019   -0.014   -0.014
## 572    SAT_1 ~~   C_REP2  0.407 -0.006  -0.006   -0.066   -0.066
## 573      Im6 ~~    SAT_3  0.403 -0.020  -0.020   -0.033   -0.033
## 574     Im13 ~~      Im6  0.401  0.016   0.016    0.038    0.038
## 575    AFCOM =~      Im4  0.399 -0.015  -0.016   -0.012   -0.012
## 576       RI =~   COM_A2  0.395 -0.050  -0.029   -0.018   -0.018
## 577    C_CR3 ~~    C_CR4  0.394 -0.226  -0.226   -0.165   -0.165
## 578     Im20 ~~   C_REP1  0.388 -0.012  -0.012   -0.033   -0.033
## 579     Im11 ~~    C_CR3  0.385  0.035   0.035    0.033    0.033
## 580   FRENCH =~    SAT_2  0.383  0.021   0.020    0.020    0.020
## 581     Im12 ~~   C_REP2  0.378  0.007   0.007    0.065    0.065
## 582     Im10 ~~    SAT_3  0.377  0.011   0.011    0.035    0.035
## 583    ATMOS  ~      SAT  0.371 -0.052  -0.036   -0.036   -0.036
## 584     Im13 ~~     Im19  0.371  0.016   0.016    0.040    0.040
## 585     DECO =~    SAT_3  0.370 -0.023  -0.028   -0.025   -0.025
## 586      Im2 ~~      Im7  0.369  0.012   0.012    0.053    0.053
## 587    SAT_2 ~~   C_REP2  0.368  0.006   0.006    0.058    0.058
## 588     Im14 ~~   C_REP2  0.367 -0.004  -0.004   -0.078   -0.078
## 589    AFCOM =~      Im6  0.367  0.022   0.025    0.021    0.021
## 590   COM_A1 ~~    C_CR4  0.359 -0.034  -0.034   -0.033   -0.033
## 591      Im1 ~~    SAT_3  0.354  0.015   0.015    0.061    0.061
## 592     FOOD =~      Im3  0.352 -0.021  -0.017   -0.013   -0.013
## 593      Im6 ~~   COM_A2  0.352  0.020   0.020    0.033    0.033
## 594    ATMOS =~     Im16  0.351 -0.027  -0.033   -0.028   -0.028
## 595      Im5 ~~     Im22  0.351  0.022   0.022    0.033    0.033
## 596 PRODQUAL =~   COM_A1  0.350  0.040   0.028    0.020    0.020
## 597   C_REP2 ~~    C_CR3  0.348  0.012   0.012    0.056    0.056
## 598     Im17 ~~   COM_A2  0.346 -0.017  -0.017   -0.061   -0.061
## 599      Im5 ~~     Im17  0.344  0.015   0.015    0.056    0.056
## 600     Im11 ~~   C_REP3  0.343  0.009   0.009    0.028    0.028
## 601   COM_A3 ~~    SAT_1  0.342  0.018   0.018    0.037    0.037
## 602   CHOICE =~   COM_A4  0.338 -0.022  -0.029   -0.017   -0.017
## 603      Im3 ~~   COM_A2  0.336 -0.014  -0.014   -0.034   -0.034
## 604      Im3 ~~   COM_A1  0.336 -0.013  -0.013   -0.033   -0.033
## 605     Im17 ~~    C_CR1  0.333 -0.021  -0.021   -0.067   -0.067
## 606   FRENCH =~      Im3  0.330 -0.016  -0.016   -0.012   -0.012
## 607      Im6 ~~    C_CR1  0.326  0.024   0.024    0.034    0.034
## 608     Im11 ~~   COM_A1  0.321 -0.022  -0.022   -0.028   -0.028
## 609   COM_A4 ~~    SAT_2  0.316  0.018   0.018    0.034    0.034
## 610    SAT_2 ~~    C_CR1  0.314 -0.021  -0.021   -0.036   -0.036
## 611   FRENCH =~   COM_A4  0.312  0.031   0.030    0.018    0.018
## 612      Im3 ~~     Im13  0.310  0.010   0.010    0.035    0.035
## 613     Im19 ~~    C_CR3  0.309  0.025   0.025    0.035    0.035
## 614   CHOICE =~    C_CR3  0.303 -0.026  -0.035   -0.017   -0.017
## 615      Im3 ~~    SAT_2  0.303 -0.009  -0.009   -0.034   -0.034
## 616     Im13 ~~      Im7  0.303 -0.014  -0.014   -0.055   -0.055
## 617      Im5 ~~   C_REP2  0.302 -0.007  -0.007   -0.046   -0.046
## 618     Im17 ~~      Im7  0.301 -0.012  -0.012   -0.099   -0.099
## 619     Im18 ~~    SAT_1  0.296 -0.012  -0.012   -0.033   -0.033
## 620     Im19 ~~    C_CR1  0.292  0.023   0.023    0.036    0.036
## 621     Im21 ~~     Im13  0.288 -0.017  -0.017   -0.032   -0.032
## 622    AFCOM =~      Im7  0.287 -0.022  -0.024   -0.020   -0.020
## 623    AFCOM =~     Im14  0.284  0.010   0.011    0.013    0.013
## 624   COM_A1 ~~    C_CR1  0.282 -0.028  -0.028   -0.031   -0.031
## 625      Im4 ~~     Im14  0.279  0.005   0.005    0.058    0.058
## 626      Im5 ~~     Im20  0.279  0.020   0.020    0.028    0.028
## 627      COI =~   C_REP3  0.279 -0.006  -0.010   -0.017   -0.017
## 628     Im17 ~~    C_CR3  0.278  0.021   0.021    0.057    0.057
## 629     Im21 ~~   COM_A4  0.277 -0.023  -0.023   -0.029   -0.029
## 630   CHOICE =~     Im17  0.275  0.022   0.028    0.023    0.023
## 631   CHOICE =~     Im18  0.275 -0.021  -0.028   -0.020   -0.020
## 632     Im22 ~~   COM_A2  0.272  0.021   0.021    0.032    0.032
## 633      Im2 ~~    C_CR4  0.271 -0.019  -0.019   -0.029   -0.029
## 634     Im21 ~~     Im16  0.271 -0.019  -0.019   -0.028   -0.028
## 635      Im4 ~~   C_REP3  0.271 -0.005  -0.005   -0.038   -0.038
## 636      COI =~      Im6  0.265 -0.011  -0.018   -0.015   -0.015
## 637      Im7 ~~    SAT_2  0.262 -0.011  -0.011   -0.049   -0.049
## 638   CHOICE =~      Im6  0.256 -0.014  -0.019   -0.016   -0.016
## 639     Im17 ~~    SAT_2  0.247  0.009   0.009    0.054    0.054
## 640     Im20 ~~     Im19  0.247  0.016   0.016    0.031    0.031
## 641      COI =~     Im12  0.243  0.011   0.018    0.016    0.016
## 642     DECO =~    SAT_1  0.242 -0.015  -0.018   -0.018   -0.018
## 643      SAT =~      Im6  0.242  0.022   0.019    0.016    0.016
## 644     Im16 ~~   C_REP1  0.239  0.009   0.009    0.025    0.025
## 645     Im18 ~~   C_REP2  0.237 -0.006  -0.006   -0.043   -0.043
## 646     DECO =~     Im11  0.231  0.019   0.024    0.021    0.021
## 647    SAT_3 ~~   C_REP1  0.230 -0.009  -0.009   -0.024   -0.024
## 648     Im10 ~~     Im19  0.230 -0.007  -0.007   -0.032   -0.032
## 649     DECO =~   COM_A4  0.229  0.019   0.024    0.014    0.014
## 650      Im4 ~~    SAT_1  0.225 -0.007  -0.007   -0.043   -0.043
## 651     Im14 ~~   C_REP1  0.224  0.004   0.004    0.034    0.034
## 652     PROF =~   C_REP2  0.222 -0.011  -0.010   -0.016   -0.016
## 653     Im20 ~~    SAT_3  0.218  0.018   0.018    0.025    0.025
## 654    SAT_3 ~~    C_CR4  0.215  0.026   0.026    0.025    0.025
## 655     Im16 ~~     Im18  0.213 -0.014  -0.014   -0.025   -0.025
## 656     Im11 ~~    SAT_2  0.212 -0.013  -0.013   -0.025   -0.025
## 657     FOOD =~   COM_A4  0.212 -0.028  -0.023   -0.013   -0.013
## 658     PROF =~    SAT_3  0.209 -0.033  -0.030   -0.026   -0.026
## 659     Im21 ~~    SAT_1  0.208  0.012   0.012    0.028    0.028
## 660     Im21 ~~    SAT_2  0.207 -0.012  -0.012   -0.026   -0.026
## 661     Im22 ~~     Im17  0.206  0.012   0.012    0.053    0.053
## 662      Im5 ~~    SAT_1  0.205 -0.012  -0.012   -0.026   -0.026
## 663    AFCOM =~    SAT_3  0.204  0.020   0.023    0.020    0.020
## 664      Im3 ~~   C_REP2  0.199 -0.004  -0.004   -0.043   -0.043
## 665      Im4 ~~   C_REP2  0.198  0.004   0.004    0.058    0.058
## 666      SAT =~   COM_A4  0.197  0.030   0.026    0.015    0.015
## 667 PRODQUAL =~    C_CR3  0.195 -0.041  -0.029   -0.014   -0.014
## 668     Im12 ~~    C_CR3  0.194  0.019   0.019    0.029    0.029
## 669      SAT =~      Im7  0.191  0.021   0.018    0.015    0.015
## 670     Im11 ~~    C_CR1  0.188 -0.023  -0.023   -0.024   -0.024
## 671     Im13 ~~   COM_A1  0.187  0.014   0.014    0.025    0.025
## 672      Im6 ~~   C_REP1  0.185 -0.007  -0.007   -0.022   -0.022
## 673       RI =~     Im20  0.180 -0.036  -0.021   -0.014   -0.014
## 674      Im4 ~~   COM_A1  0.174  0.009   0.009    0.032    0.032
## 675    BRAND =~     Im21  0.174 -0.018  -0.022   -0.016   -0.016
## 676    AFCOM =~     Im18  0.174 -0.015  -0.017   -0.012   -0.012
## 677      Im5 ~~   COM_A3  0.173 -0.017  -0.017   -0.021   -0.021
## 678    AFCOM =~    SAT_1  0.171 -0.015  -0.016   -0.016   -0.016
## 679     Im21 ~~      Im2  0.169  0.010   0.010    0.022    0.022
## 680     Im21 ~~     Im19  0.169 -0.013  -0.013   -0.024   -0.024
## 681     Im16 ~~   C_REP2  0.168 -0.006  -0.006   -0.038   -0.038
## 682   COM_A4 ~~    C_CR1  0.167  0.024   0.024    0.025    0.025
## 683   COM_A2 ~~   C_REP3  0.164 -0.007  -0.007   -0.021   -0.021
## 684     Im20 ~~     Im11  0.164  0.016   0.016    0.021    0.021
## 685     Im22 ~~    C_CR3  0.164  0.023   0.023    0.026    0.026
## 686    ATMOS =~    SAT_1  0.163  0.011   0.014    0.014    0.014
## 687       RI =~     Im18  0.162 -0.027  -0.016   -0.011   -0.011
## 688       RI =~     Im17  0.162  0.027   0.016    0.013    0.013
## 689     DECO ~~    AFCOM  0.161  0.017   0.015    0.015    0.015
## 690      Im1 ~~    C_CR3  0.161 -0.015  -0.015   -0.045   -0.045
## 691     Im16 ~~   COM_A1  0.154 -0.015  -0.015   -0.021   -0.021
## 692     Im12 ~~     Im19  0.151  0.009   0.009    0.027    0.027
## 693     Im10 ~~     Im22  0.151  0.007   0.007    0.026    0.026
## 694     Im22 ~~   COM_A4  0.151  0.017   0.017    0.024    0.024
## 695     Im14 ~~     Im11  0.150  0.006   0.006    0.027    0.027
## 696      Im2 ~~      Im6  0.146 -0.008  -0.008   -0.020   -0.020
## 697     Im14 ~~      Im1  0.145 -0.004  -0.004   -0.058   -0.058
## 698      Im3 ~~   C_REP1  0.142  0.004   0.004    0.021    0.021
## 699       RI =~    C_CR3  0.140  0.041   0.024    0.012    0.012
## 700     Im21 ~~   C_REP2  0.139 -0.005  -0.005   -0.033   -0.033
## 701      SAT =~     Im10  0.138 -0.010  -0.008   -0.010   -0.010
## 702     FOOD =~     Im19  0.138 -0.024  -0.020   -0.017   -0.017
## 703    BRAND =~    SAT_1  0.137 -0.011  -0.013   -0.013   -0.013
## 704      Im4 ~~     Im13  0.137 -0.007  -0.007   -0.032   -0.032
## 705     FOOD =~   COM_A1  0.137 -0.021  -0.017   -0.012   -0.012
## 706     PROF =~    C_CR3  0.136 -0.027  -0.024   -0.012   -0.012
## 707      Im4 ~~     Im20  0.136  0.008   0.008    0.030    0.030
## 708     Im13 ~~    C_CR1  0.134 -0.016  -0.016   -0.024   -0.024
## 709     Im17 ~~      Im6  0.133  0.008   0.008    0.037    0.037
## 710      Im3 ~~    C_CR3  0.132 -0.012  -0.012   -0.022   -0.022
## 711     Im19 ~~      Im6  0.132 -0.009  -0.009   -0.021   -0.021
## 712      Im2 ~~    C_CR3  0.128  0.013   0.013    0.020    0.020
## 713     Im12 ~~     Im18  0.126 -0.009  -0.009   -0.022   -0.022
## 714     FOOD =~      Im4  0.124 -0.013  -0.010   -0.008   -0.008
## 715       RI =~      Im2  0.123  0.018   0.011    0.008    0.008
## 716     Im17 ~~    SAT_1  0.123  0.006   0.006    0.041    0.041
## 717     Im19 ~~    C_CR4  0.122  0.016   0.016    0.021    0.021
## 718     DECO  ~      SAT  0.119 -0.057  -0.040   -0.040   -0.040
## 719      Im1 ~~      Im7  0.119 -0.007  -0.007   -0.063   -0.063
## 720     Im19 ~~      Im7  0.119  0.009   0.009    0.036    0.036
## 721   FRENCH =~     Im17  0.118 -0.014  -0.014   -0.011   -0.011
## 722   FRENCH =~     Im18  0.118  0.014   0.014    0.010    0.010
## 723      Im4 ~~     Im19  0.113 -0.006  -0.006   -0.030   -0.030
## 724     Im16 ~~    SAT_3  0.111  0.012   0.012    0.018    0.018
## 725      SAT =~   C_REP3  0.109  0.007   0.006    0.011    0.011
## 726     FOOD =~     Im21  0.109  0.018   0.015    0.011    0.011
## 727   COM_A3 ~~    C_CR4  0.109 -0.020  -0.020   -0.019   -0.019
## 728     Im18 ~~    C_CR3  0.109 -0.016  -0.016   -0.018   -0.018
## 729    AFCOM =~     Im19  0.108  0.012   0.013    0.012    0.012
## 730    AFCOM =~      Im1  0.108 -0.009  -0.010   -0.008   -0.008
## 731      COI =~   COM_A1  0.107  0.009   0.015    0.010    0.010
## 732      Im3 ~~      Im6  0.106  0.006   0.006    0.019    0.019
## 733     Im21 ~~      Im1  0.105  0.008   0.008    0.034    0.034
## 734     Im21 ~~   COM_A1  0.101  0.012   0.012    0.017    0.017
## 735      COI =~      Im7  0.100 -0.008  -0.013   -0.011   -0.011
## 736     Im17 ~~    C_CR4  0.098  0.012   0.012    0.033    0.033
## 737   CHOICE =~    SAT_3  0.098  0.012   0.016    0.014    0.014
## 738      COI =~     Im14  0.098 -0.004  -0.006   -0.007   -0.007
## 739      COI =~     Im10  0.098  0.004   0.006    0.007    0.007
## 740     FOOD =~     Im22  0.098  0.018   0.015    0.010    0.010
## 741      Im6 ~~   C_REP3  0.097 -0.004  -0.004   -0.016   -0.016
## 742      SAT =~      Im3  0.097  0.010   0.009    0.007    0.007
## 743     Im10 ~~   C_REP2  0.097 -0.002  -0.002   -0.031   -0.031
## 744     Im12 ~~   COM_A1  0.096  0.009   0.009    0.019    0.019
## 745     Im21 ~~    C_CR1  0.096  0.016   0.016    0.018    0.018
## 746       RI =~      Im6  0.094  0.019   0.011    0.010    0.010
## 747   C_REP3 ~~    C_CR1  0.093  0.007   0.007    0.017    0.017
## 748    ATMOS =~      Im6  0.092 -0.010  -0.013   -0.011   -0.011
## 749    ATMOS =~      Im7  0.092  0.012   0.015    0.012    0.012
## 750    AFCOM =~     Im10  0.092 -0.006  -0.006   -0.007   -0.007
## 751     DECO  ~    AFCOM  0.090  0.015   0.013    0.013    0.013
## 752    ATMOS =~    SAT_3  0.086 -0.011  -0.014   -0.012   -0.012
## 753      Im5 ~~   COM_A4  0.085 -0.012  -0.012   -0.015   -0.015
## 754      Im5 ~~     Im18  0.084  0.009   0.009    0.014    0.014
## 755    AFCOM =~     Im17  0.084  0.009   0.010    0.008    0.008
## 756     Im10 ~~   C_REP1  0.082  0.002   0.002    0.016    0.016
## 757      Im4 ~~     Im21  0.080  0.006   0.006    0.022    0.022
## 758   FRENCH =~    C_CR3  0.077 -0.018  -0.018   -0.009   -0.009
## 759     DECO =~     Im21  0.077 -0.011  -0.014   -0.010   -0.010
## 760      Im6 ~~    SAT_2  0.076 -0.006  -0.006   -0.016   -0.016
## 761     Im22 ~~   COM_A3  0.075  0.012   0.012    0.017    0.017
## 762     FOOD =~    C_CR3  0.073 -0.021  -0.017   -0.008   -0.008
## 763     DECO =~     Im19  0.072  0.016   0.020    0.018    0.018
## 764     DECO =~     Im16  0.072 -0.016  -0.019   -0.016   -0.016
## 765      Im3 ~~   C_REP3  0.072  0.002   0.002    0.015    0.015
## 766   FRENCH =~     Im12  0.071 -0.011  -0.010   -0.009   -0.009
## 767      Im4 ~~   C_REP1  0.070 -0.003  -0.003   -0.020   -0.020
## 768      Im7 ~~    C_CR3  0.068 -0.011  -0.011   -0.025   -0.025
## 769     Im11 ~~     Im19  0.067 -0.008  -0.008   -0.014   -0.014
## 770     Im14 ~~    SAT_3  0.066 -0.004  -0.004   -0.019   -0.019
## 771      SAT =~     Im22  0.065 -0.015  -0.013   -0.008   -0.008
## 772      Im5 ~~    C_CR1  0.065  0.013   0.013    0.014    0.014
## 773      Im5 ~~   COM_A1  0.065 -0.010  -0.010   -0.013   -0.013
## 774     Im10 ~~    C_CR3  0.065 -0.006  -0.006   -0.016   -0.016
## 775     PROF =~   COM_A4  0.063 -0.015  -0.014   -0.008   -0.008
## 776      Im5 ~~    SAT_3  0.061 -0.009  -0.009   -0.012   -0.012
## 777     Im21 ~~   COM_A2  0.060  0.010   0.010    0.013    0.013
## 778     Im16 ~~      Im6  0.060 -0.007  -0.007   -0.013   -0.013
## 779     Im20 ~~     Im16  0.059  0.009   0.009    0.014    0.014
## 780     PROF =~     Im21  0.059  0.015   0.013    0.010    0.010
## 781      Im2 ~~     Im19  0.058 -0.005  -0.005   -0.014   -0.014
## 782      Im5 ~~     Im12  0.058  0.007   0.007    0.014    0.014
## 783    ATMOS =~     Im14  0.057  0.004   0.005    0.006    0.006
## 784      Im1 ~~      Im6  0.057 -0.005  -0.005   -0.025   -0.025
## 785    ATMOS =~     Im10  0.057 -0.004  -0.005   -0.006   -0.006
## 786     Im18 ~~   COM_A3  0.057 -0.009  -0.009   -0.013   -0.013
## 787     Im16 ~~   COM_A2  0.056  0.009   0.009    0.013    0.013
## 788      Im4 ~~    SAT_2  0.055 -0.004  -0.004   -0.020   -0.020
## 789     DECO =~   COM_A1  0.055 -0.009  -0.011   -0.007   -0.007
## 790       RI =~    C_CR1  0.054 -0.024  -0.014   -0.007   -0.007
## 791     Im14 ~~   COM_A1  0.054  0.004   0.004    0.017    0.017
## 792     Im10 ~~      Im1  0.054 -0.003  -0.003   -0.027   -0.027
## 793   COM_A2 ~~   C_REP1  0.052  0.005   0.005    0.012    0.012
## 794     Im20 ~~    C_CR1  0.050 -0.012  -0.012   -0.014   -0.014
## 795       RI =~      Im3  0.041  0.009   0.005    0.004    0.004
## 796     Im14 ~~    C_CR3  0.040  0.005   0.005    0.016    0.016
## 797    SAT_1 ~~   C_REP1  0.040  0.003   0.003    0.012    0.012
## 798    BRAND =~    C_CR3  0.039 -0.010  -0.012   -0.006   -0.006
## 799       RI =~    SAT_1  0.038  0.011   0.006    0.006    0.006
## 800    AFCOM =~    C_CR1  0.037  0.010   0.011    0.006    0.006
## 801      Im6 ~~   COM_A4  0.035 -0.007  -0.007   -0.010   -0.010
## 802     FOOD ~~    AFCOM  0.035  0.005   0.007    0.007    0.007
## 803      SAT =~   C_REP2  0.034 -0.004  -0.003   -0.005   -0.005
## 804    SAT_3 ~~   C_REP2  0.034 -0.003  -0.003   -0.016   -0.016
## 805 PRODQUAL =~   COM_A4  0.032 -0.013  -0.009   -0.006   -0.006
## 806     Im20 ~~    C_CR4  0.031 -0.010  -0.010   -0.010   -0.010
## 807     Im18 ~~    SAT_2  0.030  0.004   0.004    0.010    0.010
## 808     Im18 ~~   COM_A4  0.030 -0.006  -0.006   -0.009   -0.009
## 809     DECO =~      Im2  0.026  0.005   0.006    0.005    0.005
## 810     DECO =~      Im1  0.026 -0.006  -0.007   -0.005   -0.005
## 811     Im14 ~~     Im19  0.026  0.002   0.002    0.014    0.014
## 812     PROF  ~    AFCOM  0.026  0.006   0.007    0.007    0.007
## 813    BRAND ~~      SAT  0.025  0.005   0.006    0.006    0.006
## 814   C_REP1 ~~    C_CR4  0.024  0.004   0.004    0.008    0.008
## 815      Im3 ~~    SAT_3  0.024 -0.004  -0.004   -0.009   -0.009
## 816     Im18 ~~    C_CR1  0.022  0.006   0.006    0.009    0.009
## 817     PROF =~     Im10  0.021  0.005   0.005    0.005    0.005
## 818     PROF =~     Im14  0.021 -0.005  -0.005   -0.006   -0.006
## 819     Im19 ~~   C_REP3  0.021 -0.002  -0.002   -0.008   -0.008
## 820     Im19 ~~   COM_A2  0.020 -0.005  -0.005   -0.009   -0.009
## 821       RI =~    SAT_3  0.020  0.011   0.006    0.006    0.006
## 822    BRAND ~~    AFCOM  0.020 -0.006  -0.005   -0.005   -0.005
## 823       RI =~    C_CR4  0.019 -0.015  -0.009   -0.004   -0.004
## 824      Im1 ~~     Im19  0.019 -0.003  -0.003   -0.017   -0.017
## 825      Im1 ~~    C_CR4  0.018 -0.005  -0.005   -0.015   -0.015
## 826     Im12 ~~      Im1  0.018 -0.003  -0.003   -0.017   -0.017
## 827     Im11 ~~    SAT_3  0.018 -0.005  -0.005   -0.006   -0.006
## 828   FRENCH =~      Im4  0.018  0.004   0.004    0.003    0.003
## 829     DECO =~     Im14  0.018  0.003   0.003    0.004    0.004
## 830     DECO =~     Im10  0.018 -0.003  -0.003   -0.004   -0.004
## 831      Im5 ~~   C_REP3  0.015 -0.002  -0.002   -0.006   -0.006
## 832     Im19 ~~   COM_A4  0.014 -0.004  -0.004   -0.007   -0.007
## 833   CHOICE =~   COM_A2  0.013 -0.004  -0.005   -0.003   -0.003
## 834   C_REP2 ~~    C_CR1  0.012  0.002   0.002    0.011    0.011
## 835   C_REP1 ~~    C_CR1  0.012  0.003   0.003    0.006    0.006
## 836    AFCOM =~      Im3  0.012 -0.003  -0.003   -0.002   -0.002
## 837    AFCOM =~     Im22  0.012 -0.006  -0.006   -0.004   -0.004
## 838     Im18 ~~    C_CR4  0.012 -0.005  -0.005   -0.006   -0.006
## 839     FOOD =~     Im17  0.011  0.005   0.004    0.003    0.003
## 840     FOOD =~     Im18  0.011 -0.005  -0.004   -0.003   -0.003
## 841      Im2 ~~    SAT_3  0.010 -0.003  -0.003   -0.005   -0.005
## 842     Im13 ~~    SAT_1  0.010  0.002   0.002    0.007    0.007
## 843    SAT_1 ~~    SAT_2  0.009  0.005   0.005    0.017    0.017
## 844      Im1 ~~   C_REP1  0.009 -0.001  -0.001   -0.009   -0.009
## 845      Im3 ~~     Im16  0.008 -0.002  -0.002   -0.005   -0.005
## 846      COI =~     Im21  0.008  0.002   0.004    0.003    0.003
## 847     Im21 ~~   COM_A3  0.008 -0.004  -0.004   -0.005   -0.005
## 848   CHOICE =~      Im7  0.007  0.003   0.003    0.003    0.003
## 849   COM_A3 ~~    C_CR1  0.007  0.005   0.005    0.005    0.005
## 850   FRENCH  ~    AFCOM  0.006  0.006   0.007    0.007    0.007
## 851     Im11 ~~     Im16  0.006 -0.003  -0.003   -0.004   -0.004
## 852   COM_A2 ~~   C_REP2  0.006  0.001   0.001    0.007    0.007
## 853      Im3 ~~     Im21  0.005 -0.002  -0.002   -0.004   -0.004
## 854    SAT_2 ~~    C_CR4  0.005  0.003   0.003    0.004    0.004
## 855   COM_A4 ~~   C_REP2  0.005 -0.001  -0.001   -0.007   -0.007
## 856 PRODQUAL ~~      SAT  0.004 -0.001  -0.003   -0.003   -0.003
## 857     Im21 ~~      Im6  0.003 -0.002  -0.002   -0.003   -0.003
## 858     Im13 ~~   C_REP3  0.003  0.001   0.001    0.003    0.003
## 859     Im16 ~~     Im17  0.003 -0.001  -0.001   -0.006   -0.006
## 860   COM_A2 ~~    C_CR3  0.003 -0.003  -0.003   -0.003   -0.003
## 861     FOOD =~    SAT_1  0.003 -0.002  -0.002   -0.002   -0.002
## 862   FRENCH =~     Im10  0.002  0.002   0.002    0.002    0.002
## 863   FRENCH =~     Im14  0.002 -0.002  -0.002   -0.002   -0.002
## 864     Im22 ~~    C_CR4  0.002  0.003   0.003    0.003    0.003
## 865     Im16 ~~    C_CR3  0.002 -0.002  -0.002   -0.003   -0.003
## 866 PRODQUAL =~      Im3  0.002  0.002   0.001    0.001    0.001
## 867 PRODQUAL =~     Im21  0.001  0.002   0.002    0.001    0.001
## 868      Im6 ~~    C_CR3  0.001 -0.001  -0.001   -0.002   -0.002
## 869    BRAND =~   C_REP2  0.001  0.000   0.001    0.001    0.001
## 870 PRODQUAL =~    SAT_3  0.000 -0.001  -0.001   -0.001   -0.001
## 871      COI =~     Im18  0.000  0.000  -0.001   -0.001   -0.001
## 872      COI =~     Im17  0.000  0.000   0.001    0.001    0.001
## 873      Im4 ~~    SAT_3  0.000  0.000   0.000   -0.001   -0.001
## 874      Im2 ~~   COM_A2  0.000  0.000   0.000   -0.001   -0.001
## 875     Im13 ~~    C_CR4  0.000  0.001   0.001    0.001    0.001
## 876   FRENCH =~   C_REP3  0.000  0.000   0.000    0.000    0.000
## 877     Im19 ~~   COM_A3  0.000  0.000   0.000    0.001    0.001
## 878     Im18 ~~    SAT_3  0.000  0.000   0.000   -0.001   -0.001
## 879     FOOD =~     Im12  0.000  0.000   0.000    0.000    0.000
## 880   FRENCH =~     Im19  0.000  0.000   0.000    0.000    0.000
## 881    BRAND =~   COM_A1  0.000  0.000   0.000    0.000    0.000
## 882     DECO =~    C_CR3  0.000  0.000   0.000    0.000    0.000
## 883     FOOD =~   C_REP3  0.000  0.000   0.000    0.000    0.000
## 884     Im11 ~~   COM_A4  0.000  0.000   0.000    0.000    0.000
## 885      Im5 ~~     Im13  0.000  0.000   0.000    0.000    0.000
## 886    AFCOM =~     Im21  0.000  0.000   0.000    0.000    0.000

2.4.4 full model

# missing Im8, Im15, Im9

# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2  
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "

# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7

AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4

SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH

RI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
COI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
"

2.4.5 linear regression

# # linear regression
# lm_SAT_1 <-  lm (model_SAT_1, data = survey) 
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.6 path analysis

# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 163 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       157
## 
##                                                   Used       Total
##   Number of observations                           523         553
##   Number of missing patterns                       116            
## 
## Model Test User Model:
##                                                       
##   Test statistic                              1893.114
##   Degrees of freedom                               499
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             12715.671
##   Degrees of freedom                               592
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.885
##   Tucker-Lewis Index (TLI)                       0.864
##                                                       
##   Robust Comparative Fit Index (CFI)             0.887
##   Robust Tucker-Lewis Index (TLI)                0.866
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -21220.663
##   Loglikelihood unrestricted model (H1)     -20274.106
##                                                       
##   Akaike (AIC)                               42755.327
##   Bayesian (BIC)                             43424.081
##   Sample-size adjusted Bayesian (SABIC)      42925.726
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.073
##   90 Percent confidence interval - lower         0.070
##   90 Percent confidence interval - upper         0.077
##   P-value H_0: RMSEA <= 0.050                    0.000
##   P-value H_0: RMSEA >= 0.080                    0.001
##                                                       
##   Robust RMSEA                                   0.074
##   90 Percent confidence interval - lower         0.070
##   90 Percent confidence interval - upper         0.077
##   P-value H_0: Robust RMSEA <= 0.050             0.000
##   P-value H_0: Robust RMSEA >= 0.080             0.002
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.141
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.247    0.942
##     Im4               1.049    0.025   42.358    0.000    1.309    0.967
##     Im5               0.802    0.034   23.246    0.000    1.000    0.757
##   FOOD =~                                                               
##     Im10              1.000                               0.824    0.928
##     Im14              0.999    0.035   28.444    0.000    0.822    0.952
##   ATMOS =~                                                              
##     Im20              1.000                               1.252    0.843
##     Im21              0.855    0.042   20.405    0.000    1.071    0.783
##     Im22              1.084    0.047   23.227    0.000    1.357    0.887
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.715    0.620
##     Im12              1.380    0.092   14.937    0.000    0.986    0.872
##     Im13              1.446    0.104   13.967    0.000    1.034    0.858
##   CHOICE =~                                                             
##     Im1               1.000                               1.300    0.978
##     Im2               0.882    0.033   26.957    0.000    1.147    0.897
##   PROF =~                                                               
##     Im16              1.000                               0.927    0.766
##     Im19              1.035    0.058   17.947    0.000    0.959    0.846
##   BRAND =~                                                              
##     Im17              1.000                               1.204    0.968
##     Im18              0.996    0.042   23.603    0.000    1.199    0.857
##   FRENCH =~                                                             
##     Im6               1.000                               0.977    0.812
##     Im7               1.187    0.069   17.095    0.000    1.160    0.959
##   AFCOM =~                                                              
##     COM_A1            1.000                               1.145    0.796
##     COM_A2            1.173    0.056   21.035    0.000    1.343    0.836
##     COM_A3            1.154    0.059   19.490    0.000    1.322    0.817
##     COM_A4            1.297    0.064   20.376    0.000    1.485    0.849
##   SAT =~                                                                
##     SAT_1             1.000                               0.881    0.863
##     SAT_2             0.945    0.051   18.477    0.000    0.832    0.821
##     SAT_3             0.840    0.055   15.374    0.000    0.740    0.658
##   RI =~                                                                 
##     C_REP1            1.000                               0.591    0.808
##     C_REP2            0.982    0.045   21.741    0.000    0.581    0.935
##     C_REP3            0.719    0.038   18.681    0.000    0.425    0.764
##   COI =~                                                                
##     C_CR1             1.000                               1.695    0.853
##     C_CR3             1.029    0.052   19.721    0.000    1.743    0.831
##     C_CR4             0.958    0.050   19.155    0.000    1.623    0.807
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   SAT ~                                                                 
##     DECO             -0.079    0.045   -1.764    0.078   -0.113   -0.113
##     CHOICE            0.126    0.040    3.138    0.002    0.185    0.185
##     PROF              0.549    0.083    6.643    0.000    0.577    0.577
##   AFCOM ~                                                               
##     ATMOS             0.424    0.050    8.553    0.000    0.464    0.464
##     PRODQUAL         -0.033    0.081   -0.409    0.682   -0.021   -0.021
##     FRENCH            0.240    0.055    4.364    0.000    0.205    0.205
##   RI ~                                                                  
##     SAT               0.192    0.045    4.232    0.000    0.286    0.286
##     AFCOM             0.183    0.030    6.101    0.000    0.355    0.355
##     DECO              0.006    0.029    0.190    0.850    0.012    0.012
##     FOOD              0.012    0.049    0.241    0.809    0.016    0.016
##     ATMOS             0.040    0.029    1.369    0.171    0.085    0.085
##     PRODQUAL          0.110    0.052    2.103    0.035    0.133    0.133
##     CHOICE           -0.018    0.027   -0.674    0.500   -0.041   -0.041
##     PROF             -0.023    0.066   -0.346    0.730   -0.036   -0.036
##     BRAND             0.008    0.030    0.256    0.798    0.016    0.016
##     FRENCH           -0.034    0.039   -0.882    0.378   -0.057   -0.057
##     Im8               0.050    0.036    1.371    0.170    0.085    0.089
##     Im15             -0.001    0.030   -0.042    0.966   -0.002   -0.003
##     Im9              -0.047    0.022   -2.091    0.037   -0.079   -0.107
##   COI ~                                                                 
##     SAT              -0.351    0.137   -2.571    0.010   -0.183   -0.183
##     AFCOM             0.531    0.093    5.725    0.000    0.359    0.359
##     DECO              0.016    0.093    0.174    0.862    0.012    0.012
##     FOOD             -0.059    0.155   -0.379    0.705   -0.028   -0.028
##     ATMOS             0.146    0.093    1.569    0.117    0.108    0.108
##     PRODQUAL          0.248    0.167    1.491    0.136    0.105    0.105
##     CHOICE           -0.000    0.089   -0.000    1.000   -0.000   -0.000
##     PROF             -0.194    0.208   -0.932    0.351   -0.106   -0.106
##     BRAND             0.036    0.097    0.370    0.712    0.025    0.025
##     FRENCH           -0.115    0.125   -0.921    0.357   -0.066   -0.066
##     Im8              -0.013    0.116   -0.113    0.910   -0.008   -0.008
##     Im15             -0.057    0.098   -0.586    0.558   -0.034   -0.040
##     Im9              -0.014    0.071   -0.198    0.843   -0.008   -0.011
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.425    0.052    8.163    0.000    0.414    0.414
##     ATMOS             0.740    0.084    8.814    0.000    0.473    0.473
##     PRODQUAL          0.419    0.053    7.877    0.000    0.470    0.470
##     CHOICE            0.732    0.081    8.987    0.000    0.451    0.451
##     PROF              0.770    0.073   10.478    0.000    0.666    0.666
##     BRAND             0.785    0.079    9.986    0.000    0.523    0.523
##     FRENCH            0.411    0.065    6.291    0.000    0.337    0.337
##   FOOD ~~                                                               
##     ATMOS             0.311    0.052    5.948    0.000    0.301    0.301
##     PRODQUAL          0.264    0.035    7.461    0.000    0.448    0.448
##     CHOICE            0.311    0.051    6.052    0.000    0.290    0.290
##     PROF              0.401    0.045    8.821    0.000    0.526    0.526
##     BRAND             0.322    0.049    6.639    0.000    0.325    0.325
##     FRENCH            0.473    0.049    9.744    0.000    0.588    0.588
##   ATMOS ~~                                                              
##     PRODQUAL          0.389    0.055    7.109    0.000    0.435    0.435
##     CHOICE            0.764    0.086    8.868    0.000    0.469    0.469
##     PROF              0.573    0.070    8.220    0.000    0.494    0.494
##     BRAND             0.796    0.082    9.660    0.000    0.528    0.528
##     FRENCH            0.409    0.066    6.248    0.000    0.334    0.334
##   PRODQUAL ~~                                                           
##     CHOICE            0.446    0.056    8.029    0.000    0.480    0.480
##     PROF              0.363    0.045    7.990    0.000    0.548    0.548
##     BRAND             0.483    0.055    8.838    0.000    0.561    0.561
##     FRENCH            0.219    0.039    5.620    0.000    0.313    0.313
##   CHOICE ~~                                                             
##     PROF              0.732    0.074    9.915    0.000    0.608    0.608
##     BRAND             0.806    0.080   10.029    0.000    0.515    0.515
##     FRENCH            0.275    0.062    4.471    0.000    0.217    0.217
##   PROF ~~                                                               
##     BRAND             0.680    0.068   10.004    0.000    0.609    0.609
##     FRENCH            0.356    0.053    6.662    0.000    0.393    0.393
##   BRAND ~~                                                              
##     FRENCH            0.376    0.063    5.996    0.000    0.319    0.319
##  .RI ~~                                                                 
##    .COI              -0.025    0.039   -0.626    0.532   -0.033   -0.033
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.983    0.058   85.742    0.000    4.983    3.762
##    .Im4               4.995    0.059   84.296    0.000    4.995    3.692
##    .Im5               5.049    0.058   86.541    0.000    5.049    3.823
##    .Im10              6.093    0.039  156.809    0.000    6.093    6.865
##    .Im14              6.139    0.038  161.825    0.000    6.139    7.108
##    .Im20              4.705    0.065   72.271    0.000    4.705    3.166
##    .Im21              5.163    0.060   86.177    0.000    5.163    3.775
##    .Im22              4.305    0.067   63.985    0.000    4.305    2.813
##    .Im11              5.652    0.051  111.583    0.000    5.652    4.907
##    .Im12              5.667    0.050  113.799    0.000    5.667    5.010
##    .Im13              5.451    0.053  103.064    0.000    5.451    4.525
##    .Im1               4.808    0.058   82.563    0.000    4.808    3.618
##    .Im2               4.877    0.056   86.958    0.000    4.877    3.814
##    .Im16              5.150    0.053   96.412    0.000    5.150    4.259
##    .Im19              5.158    0.050  103.703    0.000    5.158    4.551
##    .Im17              5.044    0.054   92.559    0.000    5.044    4.056
##    .Im18              4.603    0.062   74.674    0.000    4.603    3.289
##    .Im6               5.821    0.053  110.236    0.000    5.821    4.835
##    .Im7               5.759    0.053  108.103    0.000    5.759    4.760
##    .COM_A1            4.301    0.063   68.014    0.000    4.301    2.990
##    .COM_A2            3.906    0.070   55.416    0.000    3.906    2.432
##    .COM_A3            3.556    0.071   49.898    0.000    3.556    2.197
##    .COM_A4            3.482    0.077   45.431    0.000    3.482    1.992
##    .SAT_1             5.345    0.045  119.553    0.000    5.345    5.236
##    .SAT_2             5.483    0.045  123.186    0.000    5.483    5.410
##    .SAT_3             5.476    0.050  108.497    0.000    5.476    4.864
##    .C_REP1            4.221    0.274   15.421    0.000    4.221    5.767
##    .C_REP2            4.451    0.268   16.591    0.000    4.451    7.163
##    .C_REP3            4.630    0.197   23.504    0.000    4.630    8.315
##    .C_CR1             3.142    0.875    3.590    0.000    3.142    1.581
##    .C_CR3             3.747    0.900    4.161    0.000    3.747    1.786
##    .C_CR4             3.235    0.838    3.860    0.000    3.235    1.609
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##    .AFCOM             0.000                               0.000    0.000
##    .SAT               0.000                               0.000    0.000
##    .RI                0.000                               0.000    0.000
##    .COI               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.198    0.025    8.033    0.000    0.198    0.113
##    .Im4               0.118    0.025    4.748    0.000    0.118    0.064
##    .Im5               0.744    0.050   14.899    0.000    0.744    0.427
##    .Im10              0.109    0.020    5.594    0.000    0.109    0.139
##    .Im14              0.070    0.019    3.699    0.000    0.070    0.093
##    .Im20              0.640    0.059   10.906    0.000    0.640    0.290
##    .Im21              0.724    0.058   12.579    0.000    0.724    0.387
##    .Im22              0.499    0.060    8.306    0.000    0.499    0.213
##    .Im11              0.816    0.057   14.441    0.000    0.816    0.615
##    .Im12              0.306    0.039    7.864    0.000    0.306    0.240
##    .Im13              0.383    0.045    8.592    0.000    0.383    0.264
##    .Im1               0.076    0.049    1.545    0.122    0.076    0.043
##    .Im2               0.320    0.043    7.461    0.000    0.320    0.196
##    .Im16              0.604    0.051   11.825    0.000    0.604    0.413
##    .Im19              0.365    0.044    8.348    0.000    0.365    0.284
##    .Im17              0.097    0.046    2.102    0.036    0.097    0.063
##    .Im18              0.520    0.056    9.278    0.000    0.520    0.266
##    .Im6               0.495    0.055    8.939    0.000    0.495    0.341
##    .Im7               0.119    0.065    1.839    0.066    0.119    0.081
##    .COM_A1            0.758    0.060   12.599    0.000    0.758    0.366
##    .COM_A2            0.774    0.067   11.530    0.000    0.774    0.300
##    .COM_A3            0.873    0.072   12.207    0.000    0.873    0.333
##    .COM_A4            0.851    0.077   11.114    0.000    0.851    0.278
##    .SAT_1             0.266    0.035    7.682    0.000    0.266    0.255
##    .SAT_2             0.334    0.035    9.624    0.000    0.334    0.325
##    .SAT_3             0.719    0.053   13.621    0.000    0.719    0.567
##    .C_REP1            0.186    0.016   11.320    0.000    0.186    0.347
##    .C_REP2            0.049    0.011    4.658    0.000    0.049    0.127
##    .C_REP3            0.129    0.009   13.621    0.000    0.129    0.417
##    .C_CR1             1.076    0.119    9.064    0.000    1.076    0.273
##    .C_CR3             1.363    0.134   10.155    0.000    1.363    0.310
##    .C_CR4             1.412    0.128   11.025    0.000    1.412    0.349
##     DECO              1.556    0.110   14.093    0.000    1.000    1.000
##     FOOD              0.678    0.052   13.130    0.000    1.000    1.000
##     ATMOS             1.568    0.138   11.391    0.000    1.000    1.000
##     PRODQUAL          0.511    0.070    7.300    0.000    1.000    1.000
##     CHOICE            1.690    0.120   14.110    0.000    1.000    1.000
##     PROF              0.858    0.090    9.573    0.000    1.000    1.000
##     BRAND             1.450    0.106   13.655    0.000    1.000    1.000
##     FRENCH            0.955    0.096    9.930    0.000    1.000    1.000
##    .AFCOM             0.904    0.092    9.795    0.000    0.689    0.689
##    .SAT               0.462    0.051    9.139    0.000    0.595    0.595
##    .RI                0.232    0.022   10.544    0.000    0.663    0.663
##    .COI               2.332    0.219   10.636    0.000    0.812    0.812
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.6.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.4.6.2 local fit measures

# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.4.6.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##        DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI Im8
## Im3     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im4     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im5     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im10    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im14    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im20    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im21    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im22    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im11    NaN  NaN   NaN  0.385    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im12    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im13    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im1     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im2     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im16    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im19    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im17    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im18    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im6     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im7     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A4  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im8     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im15    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im9     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
##        Im15 Im9
## Im3     NaN NaN
## Im4     NaN NaN
## Im5     NaN NaN
## Im10    NaN NaN
## Im14    NaN NaN
## Im20    NaN NaN
## Im21    NaN NaN
## Im22    NaN NaN
## Im11    NaN NaN
## Im12    NaN NaN
## Im13    NaN NaN
## Im1     NaN NaN
## Im2     NaN NaN
## Im16    NaN NaN
## Im19    NaN NaN
## Im17    NaN NaN
## Im18    NaN NaN
## Im6     NaN NaN
## Im7     NaN NaN
## COM_A1  NaN NaN
## COM_A2  NaN NaN
## COM_A3  NaN NaN
## COM_A4  NaN NaN
## SAT_1   NaN NaN
## SAT_2   NaN NaN
## SAT_3   NaN NaN
## C_REP1  NaN NaN
## C_REP2  NaN NaN
## C_REP3  NaN NaN
## C_CR1   NaN NaN
## C_CR3   NaN NaN
## C_CR4   NaN NaN
## Im8     NaN NaN
## Im15    NaN NaN
## Im9     NaN NaN
2.4.6.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im8       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im15      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im9       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
##          Im8 Im15 Im9
## DECO     NaN  NaN NaN
## FOOD     NaN  NaN NaN
## ATMOS    NaN  NaN NaN
## PRODQUAL NaN  NaN NaN
## CHOICE   NaN  NaN NaN
## PROF     NaN  NaN NaN
## BRAND    NaN  NaN NaN
## FRENCH   NaN  NaN NaN
## AFCOM    NaN  NaN NaN
## SAT      NaN  NaN NaN
## RI       NaN  NaN NaN
## COI      NaN  NaN NaN
## Im8      NaN  NaN NaN
## Im15     NaN  NaN NaN
## Im9      NaN  NaN NaN
2.4.6.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im8       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im15      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im9       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
##          Im8 Im15 Im9
## DECO     NaN  NaN NaN
## FOOD     NaN  NaN NaN
## ATMOS    NaN  NaN NaN
## PRODQUAL NaN  NaN NaN
## CHOICE   NaN  NaN NaN
## PROF     NaN  NaN NaN
## BRAND    NaN  NaN NaN
## FRENCH   NaN  NaN NaN
## AFCOM    NaN  NaN NaN
## SAT      NaN  NaN NaN
## RI       NaN  NaN NaN
## COI      NaN  NaN NaN
## Im8      NaN  NaN NaN
## Im15     NaN  NaN NaN
## Im9      NaN  NaN NaN
2.4.6.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## DECO     1.000                                                               
## FOOD       NaN 1.000                                                         
## ATMOS      NaN   NaN 1.000                                                   
## PRODQUAL   NaN   NaN   NaN  1.000                                            
## CHOICE     NaN   NaN   NaN    NaN  1.000                                     
## PROF       NaN   NaN   NaN    NaN    NaN 1.000                               
## BRAND      NaN   NaN   NaN    NaN    NaN   NaN 1.000                         
## FRENCH     NaN   NaN   NaN    NaN    NaN   NaN   NaN  1.000                  
## AFCOM      NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN            
## SAT        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN      
## RI         NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## COI        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im8        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im15       NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im9        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
##            COI   Im8  Im15   Im9
## DECO                            
## FOOD                            
## ATMOS                           
## PRODQUAL                        
## CHOICE                          
## PROF                            
## BRAND                           
## FRENCH                          
## AFCOM                           
## SAT                             
## RI                              
## COI      0.812                  
## Im8        NaN 1.000            
## Im15       NaN   NaN 1.000      
## Im9        NaN   NaN   NaN 1.000
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##               DECO      FOOD    ATMOS  PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## FOOD     0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## ATMOS    0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## PRODQUAL 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## CHOICE   0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## PROF     0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## BRAND    0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## FRENCH   0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## AFCOM    0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## SAT      0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## RI       0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## COI      0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## Im8      0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## Im15     0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## Im9      0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
##             FRENCH    AFCOM       SAT        RI      COI Im8 Im15 Im9
## DECO     0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## FOOD     0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## ATMOS    0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## PRODQUAL 0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## CHOICE   0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## PROF     0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## BRAND    0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## FRENCH   0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## AFCOM    0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## SAT      0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## RI       0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## COI      0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## Im8      0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## Im15     0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
## Im9      0.7887533 0.680406 0.6175005 0.7029673 0.689651   1    1   1
psi
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO      1.000                                                               
## FOOD      0.414  1.000                                                        
## ATMOS     0.473  0.301  1.000                                                 
## PRODQUAL  0.470  0.448  0.435  1.000                                          
## CHOICE    0.451  0.290  0.469  0.480  1.000                                   
## PROF      0.666  0.526  0.494  0.548  0.608  1.000                            
## BRAND     0.523  0.325  0.528  0.561  0.515  0.609  1.000                     
## FRENCH    0.337  0.588  0.334  0.313  0.217  0.393  0.319  1.000              
## AFCOM     0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.689       
## SAT       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.595
## RI        0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## COI       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## Im8       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## Im15      0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## Im9       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
##              RI    COI    Im8   Im15    Im9
## DECO                                       
## FOOD                                       
## ATMOS                                      
## PRODQUAL                                   
## CHOICE                                     
## PROF                                       
## BRAND                                      
## FRENCH                                     
## AFCOM                                      
## SAT                                        
## RI        0.663                            
## COI      -0.033  0.812                     
## Im8       0.000  0.000  1.000              
## Im15      0.000  0.000  0.342  1.000       
## Im9       0.000  0.000  0.442  0.397  1.000
AVEpsi_fail
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO          .                                                               
## FOOD        NaN      .                                                        
## ATMOS       NaN    NaN      .                                                 
## PRODQUAL    NaN    NaN    NaN      .                                          
## CHOICE      NaN    NaN    NaN    NaN      .                                   
## PROF        NaN    NaN    NaN    NaN    NaN      .                            
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .                     
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .              
## AFCOM       NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .       
## SAT         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .
## RI          NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## COI         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im8         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im15        NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im9         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
##              RI    COI    Im8   Im15    Im9
## DECO                                       
## FOOD                                       
## ATMOS                                      
## PRODQUAL                                   
## CHOICE                                     
## PROF                                       
## BRAND                                      
## FRENCH                                     
## AFCOM                                      
## SAT                                        
## RI            .                            
## COI         NaN      .                     
## Im8         NaN    NaN      .              
## Im15        NaN    NaN    NaN      .       
## Im9         NaN    NaN    NaN    NaN      .

2.4.6.3 Modification indices

arrange(modificationindices(SEM_fit),-mi)
##          lhs op      rhs      mi    epc sepc.lv sepc.all sepc.nox
## 1       Im15  ~   CHOICE 182.606  0.497   0.646    0.542    0.542
## 2        Im8  ~     FOOD 165.135  0.649   0.534    0.509    0.509
## 3       Im15  ~     PROF 142.369  0.652   0.604    0.507    0.507
## 4        Im8  ~   FRENCH 131.378  0.492   0.481    0.458    0.458
## 5       Im15  ~    BRAND  87.499  0.374   0.451    0.378    0.378
## 6       Im15  ~       RI  86.137  1.347   0.797    0.669    0.669
## 7       Im15  ~ PRODQUAL  85.339  0.647   0.463    0.388    0.388
## 8       Im15  ~      SAT  73.509  0.492   0.433    0.363    0.363
## 9       Im15  ~    ATMOS  70.517  0.332   0.416    0.349    0.349
## 10      Im15  ~     DECO  69.835  0.321   0.400    0.336    0.336
## 11      FOOD  ~      Im8  63.988  0.217   0.264    0.277    0.264
## 12    FRENCH  ~      Im8  60.204  0.269   0.275    0.289    0.275
## 13     AFCOM =~   C_REP1  55.975  0.174   0.200    0.273    0.273
## 14    FRENCH  ~      Im9  49.676  0.189   0.193    0.263    0.193
## 15    C_REP2 ~~   C_REP3  49.318  0.103   0.103    1.291    1.291
## 16     AFCOM  ~      SAT  40.895  0.403   0.310    0.310    0.310
## 17       SAT  ~    AFCOM  40.627  0.222   0.288    0.288    0.288
## 18    CHOICE  ~     Im15  38.544  0.236   0.182    0.217    0.182
## 19     AFCOM  ~      COI  37.183 -0.808  -1.196   -1.196   -1.196
## 20     AFCOM ~~      SAT  34.958  0.217   0.335    0.335    0.335
## 21     AFCOM  ~       RI  34.443  1.874   0.968    0.968    0.968
## 22       SAT  ~       RI  31.869  0.895   0.601    0.601    0.601
## 23       Im9  ~    BRAND  31.649  0.245   0.295    0.217    0.217
## 24       Im9  ~   FRENCH  31.256  0.304   0.297    0.218    0.218
## 25    COM_A1 ~~   COM_A2  30.349  0.284   0.284    0.371    0.371
## 26       Im9  ~ PRODQUAL  27.722  0.402   0.287    0.211    0.211
## 27       SAT  ~      COI  26.144  0.287   0.552    0.552    0.552
## 28      Im15  ~    AFCOM  24.017  0.212   0.242    0.203    0.203
## 29     ATMOS =~   C_REP1  21.866  0.095   0.119    0.162    0.162
## 30       Im8  ~     PROF  19.101  0.205   0.190    0.181    0.181
## 31     BRAND =~     Im13  19.101  0.197   0.237    0.196    0.196
## 32      Im11 ~~     Im13  18.857 -0.182  -0.182   -0.326   -0.326
## 33      PROF  ~     Im15  18.511  0.113   0.122    0.146    0.122
## 34        RI =~    SAT_2  17.237  0.269   0.159    0.157    0.157
## 35    CHOICE =~     Im20  16.539 -0.162  -0.211   -0.142   -0.142
## 36  PRODQUAL  ~      Im9  15.822  0.078   0.109    0.149    0.109
## 37        RI =~     Im22  14.652 -0.331  -0.196   -0.128   -0.128
## 38     AFCOM =~   C_REP2  14.550 -0.076  -0.087   -0.139   -0.139
## 39      Im21 ~~     Im22  14.329 -0.237  -0.237   -0.394   -0.394
## 40     BRAND =~     Im12  14.102 -0.160  -0.193   -0.171   -0.171
## 41       Im8  ~       RI  13.989  0.467   0.276    0.263    0.263
## 42       Im8  ~    AFCOM  13.785  0.138   0.158    0.151    0.151
## 43    C_REP1 ~~   C_REP3  13.547 -0.049  -0.049   -0.318   -0.318
## 44    COM_A3 ~~   C_REP1  13.032  0.080   0.080    0.197    0.197
## 45      FOOD =~     Im11  12.844  0.217   0.179    0.155    0.155
## 46    CHOICE =~     Im13  12.827  0.130   0.169    0.140    0.140
## 47       SAT =~   COM_A3  12.554  0.207   0.183    0.113    0.113
## 48     AFCOM =~    SAT_2  12.377  0.102   0.116    0.115    0.115
## 49       Im8  ~      SAT  12.277  0.173   0.152    0.145    0.145
## 50      Im21 ~~   C_REP3  12.244  0.056   0.056    0.183    0.183
## 51       Im9  ~    ATMOS  12.056  0.150   0.187    0.138    0.138
## 52       SAT  ~   FRENCH  11.829  0.148   0.164    0.164    0.164
## 53     AFCOM =~   C_REP3  11.813 -0.064  -0.074   -0.133   -0.133
## 54       Im9  ~       RI  11.217  0.529   0.313    0.230    0.230
## 55      PROF =~   COM_A3  11.112  0.195   0.180    0.111    0.111
## 56     BRAND  ~      Im9  10.995  0.098   0.081    0.111    0.081
## 57      Im11 ~~     Im12  10.597  0.130   0.130    0.260    0.260
## 58       Im8  ~     DECO  10.547  0.107   0.134    0.127    0.127
## 59      Im13 ~~      Im1  10.493  0.068   0.068    0.400    0.400
## 60     ATMOS =~     Im12  10.450 -0.115  -0.144   -0.127   -0.127
## 61    C_REP1 ~~   C_REP2  10.416 -0.072  -0.072   -0.756   -0.756
## 62    COM_A1 ~~   COM_A4  10.164 -0.180  -0.180   -0.224   -0.224
## 63  PRODQUAL  ~     Im15  10.076  0.071   0.099    0.119    0.099
## 64    FRENCH  ~      COI  10.002 -0.359  -0.623   -0.623   -0.623
## 65  PRODQUAL  ~       RI   9.997 -0.553  -0.458   -0.458   -0.458
## 66    CHOICE =~   C_REP1   9.925  0.055   0.072    0.098    0.098
## 67     AFCOM =~     Im11   9.855  0.126   0.144    0.125    0.125
## 68       SAT =~    C_CR4   9.826  0.239   0.211    0.105    0.105
## 69  PRODQUAL =~    C_CR4   9.641  0.289   0.207    0.103    0.103
## 70     ATMOS =~   C_REP3   9.610 -0.051  -0.064   -0.114   -0.114
## 71    CHOICE =~     Im12   9.376 -0.105  -0.137   -0.121   -0.121
## 72     BRAND =~     Im20   9.366 -0.142  -0.171   -0.115   -0.115
## 73    COM_A3 ~~   COM_A4   9.167  0.194   0.194    0.225    0.225
## 74      Im13 ~~     Im17   9.136  0.068   0.068    0.354    0.354
## 75    CHOICE =~   C_REP3   9.111 -0.043  -0.056   -0.101   -0.101
## 76        RI =~     Im21   9.083  0.250   0.148    0.108    0.108
## 77      PROF  ~      SAT   9.064 -0.330  -0.313   -0.313   -0.313
## 78      PROF ~~      SAT   9.064 -0.152  -0.242   -0.242   -0.242
## 79      Im16 ~~     Im19   9.064  0.287   0.287    0.612    0.612
## 80     ATMOS =~    C_CR4   8.951  0.162   0.203    0.101    0.101
## 81       COI =~    SAT_2   8.908  0.061   0.103    0.101    0.101
## 82      FOOD  ~       RI   8.883  0.425   0.305    0.305    0.305
## 83      Im10 ~~      Im6   8.775 -0.042  -0.042   -0.182   -0.182
## 84     AFCOM  ~     PROF   8.643  0.225   0.182    0.182    0.182
## 85       Im4 ~~     Im17   8.327 -0.044  -0.044   -0.415   -0.415
## 86      DECO =~   COM_A3   8.160  0.115   0.144    0.089    0.089
## 87    FRENCH =~   C_REP1   8.002  0.066   0.064    0.088    0.088
## 88       SAT  ~     FOOD   7.987  0.159   0.149    0.149    0.149
## 89        RI =~   COM_A1   7.971  0.251   0.148    0.103    0.103
## 90      Im19 ~~   C_REP1   7.883 -0.045  -0.045   -0.171   -0.171
## 91       COI =~   C_REP1   7.851  0.038   0.064    0.087    0.087
## 92       Im1 ~~    SAT_2   7.828 -0.053  -0.053   -0.332   -0.332
## 93  PRODQUAL =~    C_CR1   7.719 -0.249  -0.178   -0.090   -0.090
## 94      FOOD =~      Im6   7.603 -0.303  -0.249   -0.207   -0.207
## 95     BRAND =~     Im22   7.593  0.131   0.158    0.103    0.103
## 96     AFCOM  ~   CHOICE   7.579  0.124   0.140    0.140    0.140
## 97       SAT =~   C_REP1   7.571  0.081   0.071    0.097    0.097
## 98      DECO =~     Im20   7.454 -0.114  -0.143   -0.096   -0.096
## 99     BRAND =~   COM_A3   7.093  0.113   0.136    0.084    0.084
## 100   COM_A4 ~~    SAT_1   7.080  0.084   0.084    0.176    0.176
## 101     Im22 ~~   C_REP3   7.019 -0.042  -0.042   -0.163   -0.163
## 102 PRODQUAL  ~      COI   7.005 -0.212  -0.503   -0.503   -0.503
## 103      SAT  ~      Im8   6.880  0.088   0.099    0.104    0.099
## 104     DECO ~~      SAT   6.878 -0.342  -0.403   -0.403   -0.403
## 105     DECO  ~      SAT   6.877 -0.740  -0.523   -0.523   -0.523
## 106     DECO =~    C_CR1   6.855 -0.128  -0.160   -0.080   -0.080
## 107     DECO =~   C_REP1   6.832  0.048   0.060    0.081    0.081
## 108    ATMOS  ~      COI   6.795 -0.412  -0.558   -0.558   -0.558
## 109      Im9  ~     DECO   6.761  0.109   0.135    0.100    0.100
## 110     Im15  ~      COI   6.706  0.178   0.301    0.253    0.253
## 111    BRAND =~      Im7   6.608 -0.103  -0.123   -0.102   -0.102
## 112      Im3 ~~      Im1   6.578 -0.038  -0.038   -0.308   -0.308
## 113     PROF =~    C_CR4   6.569  0.185   0.171    0.085    0.085
## 114    ATMOS =~     Im11   6.553  0.105   0.131    0.114    0.114
## 115     Im10 ~~      Im7   6.452  0.037   0.037    0.329    0.329
## 116     Im10 ~~     Im16   6.282  0.041   0.041    0.160    0.160
## 117       RI =~     Im12   6.272 -0.166  -0.098   -0.087   -0.087
## 118     Im20 ~~     Im21   6.250  0.142   0.142    0.208    0.208
## 119      SAT =~     Im12   6.193 -0.112  -0.099   -0.088   -0.088
## 120   COM_A2 ~~   COM_A3   6.190 -0.145  -0.145   -0.177   -0.177
## 121    BRAND =~      Im6   6.136  0.084   0.101    0.084    0.084
## 122    BRAND =~    C_CR4   6.117  0.131   0.158    0.079    0.079
## 123     FOOD =~   COM_A3   6.048  0.151   0.124    0.077    0.077
## 124   FRENCH =~     Im22   6.042  0.125   0.122    0.080    0.080
## 125    BRAND =~      Im4   6.035 -0.067  -0.081   -0.060   -0.060
## 126 PRODQUAL =~      Im5   6.012  0.170   0.122    0.092    0.092
## 127 PRODQUAL  ~    AFCOM   5.971 -0.136  -0.219   -0.219   -0.219
## 128 PRODQUAL ~~    AFCOM   5.971 -0.123  -0.181   -0.181   -0.181
## 129     PROF =~   C_REP3   5.927 -0.054  -0.050   -0.090   -0.090
## 130       RI =~     Im14   5.920  0.086   0.051    0.059    0.059
## 131   FRENCH =~     Im16   5.903 -0.125  -0.122   -0.101   -0.101
## 132      Im9  ~      COI   5.894  0.182   0.308    0.226    0.226
## 133    SAT_1 ~~    SAT_3   5.829  0.098   0.098    0.224    0.224
## 134     DECO =~    C_CR4   5.813  0.122   0.153    0.076    0.076
## 135   CHOICE =~      Im5   5.813  0.085   0.111    0.084    0.084
## 136     FOOD =~      Im7   5.805  0.319   0.263    0.217    0.217
## 137     DECO =~      Im7   5.790 -0.094  -0.117   -0.097   -0.097
## 138    SAT_2 ~~    SAT_3   5.753 -0.092  -0.092   -0.187   -0.187
## 139    ATMOS =~   COM_A1   5.615 -0.107  -0.134   -0.093   -0.093
## 140    AFCOM =~     Im12   5.592 -0.077  -0.089   -0.078   -0.078
## 141     Im10 ~~     Im13   5.573 -0.033  -0.033   -0.163   -0.163
## 142     DECO =~     Im22   5.482  0.100   0.125    0.081    0.081
## 143      Im9  ~    AFCOM   5.441  0.110   0.126    0.092    0.092
## 144     DECO =~   C_REP3   5.433 -0.035  -0.043   -0.078   -0.078
## 145     Im10 ~~   COM_A2   5.414  0.043   0.043    0.148    0.148
## 146   FRENCH =~     Im20   5.341 -0.115  -0.112   -0.076   -0.076
## 147     Im14 ~~     Im16   5.332 -0.037  -0.037   -0.178   -0.178
## 148     Im13 ~~      Im2   5.238 -0.048  -0.048   -0.137   -0.137
## 149    BRAND =~      Im5   5.235  0.093   0.112    0.085    0.085
## 150     Im20 ~~     Im17   5.217 -0.061  -0.061   -0.246   -0.246
## 151     PROF =~     Im20   5.188 -0.143  -0.132   -0.089   -0.089
## 152    ATMOS =~      Im5   5.177  0.089   0.111    0.084    0.084
## 153     FOOD =~   C_REP1   5.072  0.062   0.051    0.070    0.070
## 154     DECO =~      Im6   5.061  0.075   0.093    0.077    0.077
## 155     PROF =~    SAT_2   5.028  0.134   0.124    0.123    0.123
## 156     FOOD =~     Im13   4.954 -0.124  -0.102   -0.085   -0.085
## 157     Im15  ~     FOOD   4.900  0.130   0.107    0.090    0.090
## 158     PROF =~     Im12   4.838 -0.132  -0.122   -0.108   -0.108
## 159    ATMOS  ~    AFCOM   4.783 -0.263  -0.241   -0.241   -0.241
## 160    ATMOS ~~    AFCOM   4.782 -0.238  -0.200   -0.200   -0.200
## 161     DECO =~     Im18   4.776  0.097   0.120    0.086    0.086
## 162     DECO =~     Im17   4.776 -0.097  -0.121   -0.097   -0.097
## 163    SAT_3 ~~    C_CR3   4.759 -0.123  -0.123   -0.125   -0.125
## 164   FRENCH  ~      SAT   4.717  0.140   0.126    0.126    0.126
## 165   FRENCH ~~      SAT   4.717  0.065   0.097    0.097    0.097
## 166    BRAND =~   C_REP3   4.703 -0.034  -0.041   -0.074   -0.074
## 167   FRENCH =~   C_REP2   4.701 -0.042  -0.041   -0.065   -0.065
## 168     Im19 ~~   C_REP2   4.680  0.027   0.027    0.199    0.199
## 169     Im20 ~~      Im6   4.664 -0.068  -0.068   -0.120   -0.120
## 170   C_REP2 ~~    C_CR4   4.629 -0.046  -0.046   -0.174   -0.174
## 171   COM_A3 ~~   C_REP2   4.626 -0.035  -0.035   -0.171   -0.171
## 172      Im3 ~~   COM_A4   4.625  0.055   0.055    0.134    0.134
## 173   COM_A1 ~~    SAT_3   4.601  0.084   0.084    0.114    0.114
## 174     Im11 ~~      Im6   4.589 -0.068  -0.068   -0.107   -0.107
## 175     Im22 ~~   C_REP1   4.583  0.041   0.041    0.134    0.134
## 176    BRAND =~    SAT_2   4.558  0.065   0.079    0.078    0.078
## 177     Im22 ~~      Im1   4.528  0.053   0.053    0.274    0.274
## 178      Im4 ~~     Im18   4.526  0.039   0.039    0.159    0.159
## 179     Im20 ~~     Im13   4.492  0.067   0.067    0.135    0.135
## 180 PRODQUAL =~      Im2   4.481 -0.130  -0.093   -0.073   -0.073
## 181      Im9  ~     FOOD   4.452  0.135   0.111    0.082    0.082
## 182      SAT =~   COM_A2   4.449 -0.118  -0.104   -0.065   -0.065
## 183    SAT_1 ~~   C_REP2   4.442 -0.022  -0.022   -0.196   -0.196
## 184      Im4 ~~   COM_A3   4.418  0.052   0.052    0.162    0.162
## 185     Im22 ~~    SAT_3   4.400 -0.078  -0.078   -0.130   -0.130
## 186      Im9  ~     PROF   4.377  0.124   0.115    0.085    0.085
## 187     PROF =~   COM_A2   4.354 -0.117  -0.108   -0.067   -0.067
## 188     Im22 ~~     Im11   4.339  0.079   0.079    0.124    0.124
## 189     Im13 ~~     Im16   4.324 -0.062  -0.062   -0.130   -0.130
## 190      Im3 ~~      Im5   4.300 -0.068  -0.068   -0.178   -0.178
## 191      SAT =~   COM_A4   4.286  0.123   0.109    0.062    0.062
## 192      SAT =~    C_CR1   4.284 -0.152  -0.134   -0.067   -0.067
## 193    BRAND =~    C_CR1   4.271 -0.106  -0.127   -0.064   -0.064
## 194     PROF =~      Im1   4.243 -0.191  -0.177   -0.133   -0.133
## 195     PROF =~      Im2   4.243  0.168   0.156    0.122    0.122
## 196     Im22 ~~   C_REP2   4.232 -0.030  -0.030   -0.189   -0.189
## 197     Im11 ~~      Im1   4.230 -0.052  -0.052   -0.211   -0.211
## 198      SAT =~   C_REP2   4.230 -0.051  -0.045   -0.072   -0.072
## 199   FRENCH =~    C_CR4   4.178  0.135   0.132    0.065    0.065
## 200    AFCOM =~      Im5   4.144  0.078   0.089    0.068    0.068
## 201       RI =~   COM_A2   4.115 -0.191  -0.113   -0.070   -0.070
## 202      Im1 ~~   C_REP3   4.114 -0.021  -0.021   -0.215   -0.215
## 203     Im14 ~~      Im6   4.087  0.028   0.028    0.152    0.152
## 204     PROF =~    C_CR1   4.082 -0.140  -0.130   -0.065   -0.065
## 205 PRODQUAL =~      Im1   4.048  0.140   0.100    0.075    0.075
## 206       RI =~      Im5   4.031  0.148   0.087    0.066    0.066
## 207    ATMOS =~      Im4   4.022 -0.052  -0.065   -0.048   -0.048
## 208     FOOD =~    C_CR4   4.017  0.155   0.128    0.064    0.064
## 209     DECO =~   COM_A2   3.972 -0.077  -0.096   -0.060   -0.060
## 210     Im12 ~~      Im7   3.960  0.046   0.046    0.242    0.242
## 211     PROF =~    SAT_1   3.932 -0.123  -0.114   -0.112   -0.112
## 212 PRODQUAL =~   C_REP3   3.918 -0.055  -0.040   -0.071   -0.071
## 213      Im4 ~~    C_CR1   3.904 -0.060  -0.060   -0.168   -0.168
## 214     PROF =~   C_REP1   3.901  0.054   0.050    0.068    0.068
## 215      Im5 ~~      Im6   3.873 -0.060  -0.060   -0.098   -0.098
## 216      Im3 ~~      Im4   3.857  0.145   0.145    0.947    0.947
## 217   FRENCH =~   COM_A3   3.843  0.108   0.105    0.065    0.065
## 218   CHOICE =~   COM_A3   3.821  0.075   0.097    0.060    0.060
## 219      Im3 ~~      Im2   3.811  0.029   0.029    0.115    0.115
## 220    SAT_2 ~~   C_REP1   3.809  0.028   0.028    0.112    0.112
## 221     Im20 ~~     Im22   3.733  0.150   0.150    0.266    0.266
## 222   CHOICE ~~    AFCOM   3.721  0.092   0.074    0.074    0.074
## 223   CHOICE  ~    AFCOM   3.721  0.102   0.090    0.090    0.090
## 224      Im2 ~~    SAT_2   3.720  0.036   0.036    0.111    0.111
## 225      Im4 ~~      Im6   3.719  0.034   0.034    0.142    0.142
## 226      Im4 ~~     Im11   3.709 -0.042  -0.042   -0.137   -0.137
## 227     FOOD =~      Im5   3.638  0.106   0.087    0.066    0.066
## 228     Im20 ~~   COM_A4   3.626  0.084   0.084    0.114    0.114
## 229      SAT =~     Im13   3.580  0.091   0.080    0.067    0.067
## 230     Im11 ~~   C_REP1   3.565  0.037   0.037    0.095    0.095
## 231   COM_A1 ~~    SAT_1   3.546 -0.053  -0.053   -0.118   -0.118
## 232     Im22 ~~    SAT_1   3.543  0.050   0.050    0.138    0.138
## 233     Im12 ~~    SAT_3   3.514  0.054   0.054    0.116    0.116
## 234    AFCOM =~     Im20   3.501 -0.093  -0.107   -0.072   -0.072
## 235      Im8  ~    ATMOS   3.500  0.064   0.080    0.076    0.076
## 236   COM_A4 ~~   C_REP1   3.485  0.042   0.042    0.105    0.105
## 237     Im13 ~~   C_REP2   3.438  0.022   0.022    0.163    0.163
## 238     Im14 ~~    SAT_2   3.365  0.022   0.022    0.146    0.146
## 239 PRODQUAL =~    SAT_2   3.351  0.096   0.069    0.068    0.068
## 240     Im10 ~~    C_CR1   3.299  0.043   0.043    0.126    0.126
## 241    ATMOS =~   COM_A4   3.291  0.093   0.117    0.067    0.067
## 242     Im11 ~~     Im17   3.272 -0.049  -0.049   -0.173   -0.173
## 243      Im3 ~~     Im17   3.256  0.028   0.028    0.202    0.202
## 244      Im8  ~ PRODQUAL   3.239  0.109   0.078    0.074    0.074
## 245     Im17 ~~   C_REP1   3.216 -0.024  -0.024   -0.180   -0.180
## 246      Im1 ~~    SAT_1   3.212  0.033   0.033    0.234    0.234
## 247     Im22 ~~   COM_A1   3.209 -0.070  -0.070   -0.113   -0.113
## 248     Im14 ~~      Im7   3.169 -0.026  -0.026   -0.284   -0.284
## 249     Im20 ~~    SAT_1   3.168 -0.049  -0.049   -0.118   -0.118
## 250      Im5 ~~      Im1   3.150  0.043   0.043    0.182    0.182
## 251     Im14 ~~    C_CR1   3.145 -0.041  -0.041   -0.148   -0.148
## 252     Im11 ~~    SAT_1   3.133  0.049   0.049    0.105    0.105
## 253     PROF  ~    AFCOM   3.106  0.064   0.079    0.079    0.079
## 254     PROF ~~    AFCOM   3.106  0.058   0.066    0.066    0.066
## 255     Im20 ~~   C_REP2   3.101  0.026   0.026    0.145    0.145
## 256      COI =~   C_REP2   3.084 -0.019  -0.033   -0.053   -0.053
## 257     Im13 ~~   COM_A2   3.074 -0.060  -0.060   -0.110   -0.110
## 258     Im16 ~~    SAT_1   3.070 -0.047  -0.047   -0.117   -0.117
## 259   COM_A3 ~~   C_REP3   3.054 -0.032  -0.032   -0.094   -0.094
## 260      COI =~     Im13   2.931 -0.039  -0.067   -0.055   -0.055
## 261     PROF =~     Im13   2.905  0.108   0.100    0.083    0.083
## 262       RI =~     Im10   2.903 -0.061  -0.036   -0.040   -0.040
## 263     Im16 ~~   C_REP3   2.900 -0.026  -0.026   -0.092   -0.092
## 264     FOOD =~    SAT_2   2.872  0.071   0.059    0.058    0.058
## 265     Im13 ~~    SAT_2   2.871  0.039   0.039    0.110    0.110
## 266     PROF  ~      COI   2.858  0.112   0.204    0.204    0.204
## 267    AFCOM =~    C_CR4   2.852  0.106   0.121    0.060    0.060
## 268    AFCOM =~     Im16   2.849 -0.066  -0.076   -0.063   -0.063
## 269      Im5 ~~   COM_A2   2.839  0.068   0.068    0.089    0.089
## 270     Im13 ~~   C_REP1   2.836 -0.027  -0.027   -0.101   -0.101
## 271      Im2 ~~     Im17   2.835  0.030   0.030    0.170    0.170
## 272      SAT  ~    ATMOS   2.834  0.064   0.091    0.091    0.091
## 273     Im18 ~~   COM_A1   2.811 -0.056  -0.056   -0.090   -0.090
## 274      Im2 ~~     Im16   2.794  0.041   0.041    0.093    0.093
## 275      Im5 ~~   C_REP1   2.784  0.031   0.031    0.084    0.084
## 276    ATMOS =~    C_CR1   2.783 -0.087  -0.109   -0.055   -0.055
## 277     Im12 ~~      Im6   2.763 -0.040  -0.040   -0.102   -0.102
## 278     Im10 ~~     Im12   2.744  0.022   0.022    0.119    0.119
## 279 PRODQUAL =~      Im4   2.735 -0.076  -0.054   -0.040   -0.040
## 280     Im18 ~~      Im6   2.731  0.044   0.044    0.087    0.087
## 281     FOOD =~    C_CR1   2.725 -0.123  -0.101   -0.051   -0.051
## 282    SAT_1 ~~    C_CR4   2.722  0.067   0.067    0.109    0.109
## 283     Im19 ~~   COM_A1   2.719  0.053   0.053    0.101    0.101
## 284    ATMOS =~   C_REP2   2.704 -0.028  -0.035   -0.057   -0.057
## 285      SAT =~   COM_A1   2.689  0.087   0.077    0.054    0.054
## 286   CHOICE =~     Im22   2.667  0.066   0.086    0.056    0.056
## 287      Im7 ~~   COM_A1   2.653 -0.050  -0.050   -0.167   -0.167
## 288    ATMOS =~     Im13   2.649  0.061   0.077    0.064    0.064
## 289   FRENCH =~     Im11   2.636  0.077   0.076    0.066    0.066
## 290     Im22 ~~    SAT_2   2.621 -0.045  -0.045   -0.109   -0.109
## 291      SAT =~      Im5   2.615  0.085   0.075    0.057    0.057
## 292       RI =~     Im16   2.613 -0.135  -0.080   -0.066   -0.066
## 293    AFCOM  ~     Im15   2.578  0.062   0.054    0.064    0.054
## 294      Im3 ~~     Im11   2.576  0.036   0.036    0.090    0.090
## 295      SAT  ~      Im9   2.560  0.041   0.047    0.064    0.047
## 296   COM_A1 ~~   C_REP2   2.551  0.024   0.024    0.124    0.124
## 297   CHOICE =~     Im19   2.546 -0.083  -0.108   -0.096   -0.096
## 298   CHOICE =~     Im16   2.546  0.080   0.105    0.086    0.086
## 299   COM_A1 ~~   COM_A3   2.527 -0.083  -0.083   -0.102   -0.102
## 300     Im14 ~~     Im12   2.506 -0.020  -0.020   -0.138   -0.138
## 301     FOOD =~   C_REP2   2.497 -0.036  -0.030   -0.048   -0.048
## 302   COM_A4 ~~    C_CR4   2.487  0.102   0.102    0.093    0.093
## 303      Im4 ~~      Im1   2.465  0.023   0.023    0.240    0.240
## 304      Im7 ~~   C_REP2   2.451 -0.018  -0.018   -0.238   -0.238
## 305     Im21 ~~    C_CR4   2.443  0.088   0.088    0.087    0.087
## 306     Im14 ~~   COM_A2   2.437 -0.028  -0.028   -0.119   -0.119
## 307      Im3 ~~   COM_A3   2.435 -0.039  -0.039   -0.095   -0.095
## 308    AFCOM =~      Im2   2.435  0.043   0.049    0.038    0.038
## 309    ATMOS =~   COM_A3   2.431  0.078   0.097    0.060    0.060
## 310     DECO =~     Im12   2.430 -0.055  -0.069   -0.061   -0.061
## 311   CHOICE  ~       RI   2.424  0.408   0.186    0.186    0.186
## 312      Im2 ~~   C_REP2   2.419 -0.015  -0.015   -0.119   -0.119
## 313     Im10 ~~     Im11   2.406  0.027   0.027    0.090    0.090
## 314      Im2 ~~    C_CR1   2.398  0.055   0.055    0.093    0.093
## 315     Im11 ~~   C_REP2   2.388 -0.023  -0.023   -0.113   -0.113
## 316   FRENCH =~   COM_A2   2.386 -0.082  -0.080   -0.050   -0.050
## 317   FRENCH =~      Im1   2.384 -0.054  -0.053   -0.040   -0.040
## 318      Im3 ~~     Im22   2.371  0.034   0.034    0.107    0.107
## 319    AFCOM =~      Im7   2.343 -0.065  -0.074   -0.061   -0.061
## 320   CHOICE =~    C_CR4   2.322  0.074   0.096    0.048    0.048
## 321     Im14 ~~     Im20   2.315 -0.025  -0.025   -0.118   -0.118
## 322      SAT =~     Im14   2.300  0.038   0.034    0.039    0.039
## 323       RI =~    SAT_1   2.296 -0.099  -0.059   -0.058   -0.058
## 324      Im1 ~~     Im17   2.292 -0.028  -0.028   -0.324   -0.324
## 325      COI =~     Im11   2.278  0.040   0.068    0.059    0.059
## 326     Im20 ~~      Im1   2.247 -0.038  -0.038   -0.173   -0.173
## 327    SAT_2 ~~    C_CR3   2.241  0.063   0.063    0.093    0.093
## 328     Im12 ~~     Im16   2.235  0.042   0.042    0.097    0.097
## 329      COI =~      Im2   2.235  0.026   0.044    0.034    0.034
## 330   FRENCH =~    C_CR1   2.234 -0.095  -0.093   -0.047   -0.047
## 331     Im21 ~~    C_CR3   2.227 -0.085  -0.085   -0.086   -0.086
## 332   C_REP3 ~~    C_CR3   2.223 -0.035  -0.035   -0.084   -0.084
## 333   FRENCH =~   COM_A1   2.220 -0.075  -0.073   -0.051   -0.051
## 334     FOOD =~     Im20   2.215 -0.085  -0.070   -0.047   -0.047
## 335      COI =~      Im1   2.207 -0.029  -0.049   -0.037   -0.037
## 336     Im20 ~~   COM_A1   2.199 -0.059  -0.059   -0.084   -0.084
## 337     FOOD =~      Im1   2.177 -0.064  -0.053   -0.040   -0.040
## 338     Im14 ~~   COM_A3   2.174  0.027   0.027    0.111    0.111
## 339   COM_A1 ~~    C_CR3   2.150  0.086   0.086    0.085    0.085
## 340   COM_A3 ~~    SAT_1   2.146  0.045   0.045    0.094    0.094
## 341   CHOICE =~     Im21   2.143  0.057   0.074    0.054    0.054
## 342      Im2 ~~   C_REP1   2.122  0.019   0.019    0.077    0.077
## 343    SAT_1 ~~    C_CR1   2.114 -0.056  -0.056   -0.104   -0.104
## 344     Im22 ~~     Im13   2.101 -0.045  -0.045   -0.103   -0.103
## 345      Im7 ~~   COM_A2   2.095 -0.047  -0.047   -0.154   -0.154
## 346    BRAND  ~       RI   2.046 -0.286  -0.141   -0.141   -0.141
## 347   COM_A2 ~~    SAT_2   2.029 -0.043  -0.043   -0.085   -0.085
## 348     Im11 ~~      Im2   2.025  0.037   0.037    0.072    0.072
## 349     Im14 ~~   C_REP3   2.024  0.010   0.010    0.103    0.103
## 350     Im18 ~~   C_REP1   2.016  0.023   0.023    0.075    0.075
## 351 PRODQUAL =~     Im16   2.011 -0.124  -0.088   -0.073   -0.073
## 352     Im22 ~~     Im19   2.000 -0.044  -0.044   -0.103   -0.103
## 353      Im5 ~~    SAT_2   1.989  0.039   0.039    0.077    0.077
## 354      Im5 ~~     Im16   1.986 -0.049  -0.049   -0.074   -0.074
## 355    AFCOM =~    SAT_1   1.973  0.040   0.045    0.044    0.044
## 356      Im4 ~~   COM_A4   1.957 -0.035  -0.035   -0.111   -0.111
## 357     PROF =~      Im7   1.948 -0.088  -0.081   -0.067   -0.067
## 358      SAT =~     Im20   1.946 -0.077  -0.068   -0.046   -0.046
## 359   COM_A2 ~~    SAT_3   1.940  0.057   0.057    0.077    0.077
## 360      Im9  ~      SAT   1.925  0.087   0.076    0.056    0.056
## 361     Im22 ~~     Im12   1.911 -0.040  -0.040   -0.102   -0.102
## 362     FOOD ~~      SAT   1.893  0.033   0.058    0.058    0.058
## 363     FOOD  ~      SAT   1.893  0.071   0.075    0.075    0.075
## 364     Im13 ~~    SAT_3   1.884 -0.043  -0.043   -0.082   -0.082
## 365   CHOICE =~     Im10   1.880 -0.023  -0.029   -0.033   -0.033
## 366   CHOICE =~     Im14   1.880  0.023   0.029    0.034    0.034
## 367 PRODQUAL =~   C_REP2   1.876  0.039   0.028    0.045    0.045
## 368    BRAND =~      Im3   1.843  0.036   0.044    0.033    0.033
## 369      COI =~     Im16   1.842 -0.037  -0.062   -0.051   -0.051
## 370 PRODQUAL =~     Im17   1.831  0.123   0.088    0.070    0.070
## 371 PRODQUAL =~     Im18   1.831 -0.122  -0.087   -0.062   -0.062
## 372   FRENCH =~    SAT_3   1.821  0.061   0.060    0.053    0.053
## 373     Im12 ~~   COM_A4   1.819 -0.045  -0.045   -0.089   -0.089
## 374    ATMOS  ~     Im15   1.799  0.053   0.043    0.051    0.043
## 375      SAT =~     Im17   1.793  0.061   0.053    0.043    0.043
## 376     Im22 ~~      Im2   1.763 -0.033  -0.033   -0.083   -0.083
## 377      SAT =~     Im18   1.744 -0.070  -0.062   -0.044   -0.044
## 378     Im17 ~~   COM_A1   1.735  0.036   0.036    0.133    0.133
## 379   COM_A4 ~~    SAT_3   1.731 -0.058  -0.058   -0.074   -0.074
## 380     Im12 ~~     Im13   1.694  0.095   0.095    0.277    0.277
## 381       RI =~     Im11   1.683  0.103   0.061    0.053    0.053
## 382     Im20 ~~     Im19   1.679  0.041   0.041    0.084    0.084
## 383   COM_A3 ~~    SAT_2   1.637  0.041   0.041    0.076    0.076
## 384      Im4 ~~      Im2   1.633 -0.019  -0.019   -0.095   -0.095
## 385     Im20 ~~   COM_A2   1.629 -0.053  -0.053   -0.075   -0.075
## 386    BRAND =~   C_REP1   1.607  0.025   0.030    0.040    0.040
## 387 PRODQUAL =~      Im7   1.597  0.090   0.064    0.053    0.053
## 388 PRODQUAL =~      Im6   1.597 -0.076  -0.054   -0.045   -0.045
## 389     Im10 ~~    SAT_2   1.596 -0.016  -0.016   -0.083   -0.083
## 390   COM_A2 ~~   COM_A4   1.589 -0.081  -0.081   -0.100   -0.100
## 391     Im16 ~~    C_CR4   1.582 -0.067  -0.067   -0.073   -0.073
## 392    BRAND  ~     Im15   1.578  0.042   0.035    0.042    0.035
## 393     Im10 ~~     Im20   1.548  0.021   0.021    0.080    0.080
## 394     Im13 ~~     Im18   1.542 -0.033  -0.033   -0.075   -0.075
## 395 PRODQUAL =~    SAT_1   1.540 -0.064  -0.046   -0.045   -0.045
## 396   C_REP3 ~~    C_CR4   1.539  0.029   0.029    0.068    0.068
## 397      Im7 ~~    SAT_3   1.537  0.036   0.036    0.125    0.125
## 398      SAT =~      Im4   1.500 -0.041  -0.037   -0.027   -0.027
## 399     FOOD =~     Im16   1.494 -0.083  -0.069   -0.057   -0.057
## 400     Im14 ~~      Im2   1.491  0.013   0.013    0.089    0.089
## 401      Im2 ~~    SAT_1   1.463 -0.022  -0.022   -0.076   -0.076
## 402      Im1 ~~   COM_A4   1.452 -0.035  -0.035   -0.137   -0.137
## 403     FOOD =~      Im2   1.452  0.047   0.038    0.030    0.030
## 404    ATMOS =~   COM_A2   1.446 -0.058  -0.072   -0.045   -0.045
## 405     Im21 ~~     Im18   1.446 -0.039  -0.039   -0.064   -0.064
## 406      Im5 ~~      Im7   1.435  0.034   0.034    0.115    0.115
## 407   FRENCH =~      Im2   1.429  0.037   0.036    0.028    0.028
## 408     DECO =~     Im13   1.412  0.045   0.056    0.046    0.046
## 409      Im2 ~~     Im18   1.408 -0.026  -0.026   -0.063   -0.063
## 410      Im3 ~~     Im18   1.392 -0.022  -0.022   -0.070   -0.070
## 411    AFCOM  ~     FOOD   1.390  0.094   0.068    0.068    0.068
## 412 PRODQUAL =~   COM_A2   1.387 -0.084  -0.060   -0.037   -0.037
## 413      Im2 ~~   C_REP3   1.386  0.013   0.013    0.061    0.061
## 414    ATMOS =~    SAT_2   1.380  0.034   0.042    0.042    0.042
## 415      Im3 ~~    C_CR1   1.380  0.036   0.036    0.079    0.079
## 416      Im7 ~~   C_REP3   1.371  0.014   0.014    0.117    0.117
## 417     Im12 ~~   COM_A3   1.362 -0.039  -0.039   -0.075   -0.075
## 418   FRENCH =~    SAT_1   1.359  0.039   0.038    0.037    0.037
## 419      Im1 ~~   C_REP2   1.349  0.011   0.011    0.185    0.185
## 420   FRENCH  ~     Im15   1.325  0.035   0.036    0.043    0.036
## 421      Im7 ~~   COM_A4   1.320  0.040   0.040    0.124    0.124
## 422     PROF  ~      Im8   1.314  0.034   0.037    0.039    0.037
## 423    ATMOS =~     Im17   1.312 -0.054  -0.067   -0.054   -0.054
## 424    ATMOS =~     Im18   1.312  0.053   0.067    0.048    0.048
## 425     Im16 ~~      Im7   1.310 -0.033  -0.033   -0.123   -0.123
## 426   C_REP1 ~~    C_CR3   1.300  0.033   0.033    0.065    0.065
## 427      Im4 ~~    C_CR3   1.291  0.037   0.037    0.092    0.092
## 428     Im14 ~~     Im13   1.286  0.015   0.015    0.095    0.095
## 429   COM_A1 ~~    C_CR1   1.282 -0.062  -0.062   -0.069   -0.069
## 430    ATMOS =~    C_CR3   1.272 -0.062  -0.078   -0.037   -0.037
## 431     Im12 ~~     Im17   1.270 -0.024  -0.024   -0.138   -0.138
## 432     Im12 ~~   COM_A2   1.270  0.036   0.036    0.073    0.073
## 433   COM_A4 ~~   C_REP3   1.269 -0.021  -0.021   -0.062   -0.062
## 434     Im20 ~~    SAT_2   1.258  0.032   0.032    0.068    0.068
## 435     Im21 ~~    SAT_3   1.256  0.043   0.043    0.059    0.059
## 436      SAT =~      Im1   1.251 -0.063  -0.056   -0.042   -0.042
## 437     Im12 ~~   C_REP1   1.249 -0.017  -0.017   -0.070   -0.070
## 438   COM_A1 ~~   C_REP3   1.245  0.018   0.018    0.059    0.059
## 439      Im8  ~      COI   1.231 -0.066  -0.111   -0.106   -0.106
## 440      SAT =~     Im19   1.224 -0.084  -0.074   -0.065   -0.065
## 441     Im10 ~~   C_REP3   1.223 -0.008  -0.008   -0.066   -0.066
## 442     Im19 ~~    SAT_3   1.222 -0.034  -0.034   -0.067   -0.067
## 443      Im5 ~~     Im14   1.221  0.018   0.018    0.077    0.077
## 444      Im6 ~~      Im7   1.217  0.401   0.401    1.652    1.652
## 445   FRENCH ~~    AFCOM   1.216 -0.081  -0.087   -0.087   -0.087
## 446   FRENCH  ~    AFCOM   1.216 -0.090  -0.105   -0.105   -0.105
## 447    BRAND  ~      Im8   1.215 -0.042  -0.035   -0.037   -0.035
## 448     Im12 ~~    SAT_1   1.214 -0.023  -0.023   -0.081   -0.081
## 449      Im6 ~~   C_REP2   1.207  0.013   0.013    0.084    0.084
## 450    AFCOM =~      Im6   1.205  0.041   0.047    0.039    0.039
## 451      Im2 ~~   COM_A3   1.197  0.032   0.032    0.060    0.060
## 452      Im1 ~~   COM_A1   1.197  0.028   0.028    0.118    0.118
## 453     Im19 ~~    SAT_2   1.188  0.026   0.026    0.074    0.074
## 454      SAT  ~     Im15   1.185  0.032   0.036    0.043    0.036
## 455     Im18 ~~   C_REP3   1.181 -0.015  -0.015   -0.057   -0.057
## 456     Im12 ~~    C_CR1   1.177 -0.044  -0.044   -0.077   -0.077
## 457     Im16 ~~    C_CR1   1.171  0.055   0.055    0.068    0.068
## 458     PROF =~      Im4   1.159 -0.053  -0.050   -0.037   -0.037
## 459    AFCOM =~     Im21   1.159  0.052   0.059    0.043    0.043
## 460   COM_A1 ~~    SAT_2   1.154  0.031   0.031    0.062    0.062
## 461 PRODQUAL =~   COM_A3   1.153  0.080   0.057    0.035    0.035
## 462    BRAND =~   COM_A2   1.147 -0.044  -0.053   -0.033   -0.033
## 463   CHOICE =~   COM_A1   1.139  0.037   0.048    0.034    0.034
## 464     Im14 ~~     Im17   1.130  0.012   0.012    0.150    0.150
## 465   COM_A4 ~~    C_CR3   1.125 -0.070  -0.070   -0.065   -0.065
## 466   COM_A2 ~~    C_CR1   1.120  0.061   0.061    0.067    0.067
## 467      SAT =~     Im11   1.114  0.059   0.052    0.045    0.045
## 468    ATMOS ~~      SAT   1.112  0.041   0.048    0.048    0.048
## 469    ATMOS  ~      SAT   1.112  0.089   0.062    0.062    0.062
## 470    BRAND =~     Im16   1.106 -0.056  -0.067   -0.056   -0.056
## 471   CHOICE  ~      COI   1.103  0.102   0.133    0.133    0.133
## 472      SAT =~      Im2   1.102  0.053   0.046    0.036    0.036
## 473    AFCOM =~    C_CR1   1.100 -0.064  -0.073   -0.037   -0.037
## 474     FOOD =~    SAT_3   1.099  0.058   0.047    0.042    0.042
## 475     Im13 ~~    C_CR3   1.096 -0.049  -0.049   -0.068   -0.068
## 476      Im5 ~~      Im2   1.095 -0.026  -0.026   -0.053   -0.053
## 477     PROF  ~       RI   1.090  0.184   0.117    0.117    0.117
## 478     Im11 ~~   COM_A3   1.075  0.046   0.046    0.054    0.054
## 479      Im6 ~~   COM_A1   1.075  0.034   0.034    0.055    0.055
## 480    AFCOM  ~     DECO   1.071  0.049   0.053    0.053    0.053
## 481     Im21 ~~     Im11   1.067 -0.040  -0.040   -0.052   -0.052
## 482     Im12 ~~    SAT_2   1.067 -0.022  -0.022   -0.070   -0.070
## 483      Im3 ~~     Im12   1.063 -0.018  -0.018   -0.071   -0.071
## 484    AFCOM  ~      Im8   1.061  0.045   0.039    0.041    0.039
## 485     Im22 ~~     Im18   1.054  0.033   0.033    0.064    0.064
## 486     Im12 ~~    C_CR3   1.050  0.045   0.045    0.069    0.069
## 487      Im3 ~~   COM_A2   1.048 -0.025  -0.025   -0.063   -0.063
## 488     PROF =~      Im5   1.047  0.070   0.064    0.049    0.049
## 489    AFCOM =~      Im1   1.043 -0.028  -0.033   -0.024   -0.024
## 490      SAT =~     Im22   1.039 -0.056  -0.050   -0.032   -0.032
## 491     Im11 ~~      Im7   1.031  0.030   0.030    0.098    0.098
## 492      Im5 ~~     Im19   1.017 -0.030  -0.030   -0.058   -0.058
## 493      Im1 ~~   COM_A3   1.014 -0.029  -0.029   -0.111   -0.111
## 494     Im17 ~~   COM_A4   1.004 -0.031  -0.031   -0.106   -0.106
## 495   FRENCH =~   COM_A4   1.003  0.057   0.055    0.032    0.032
## 496      Im1 ~~     Im18   0.979  0.021   0.021    0.107    0.107
## 497      Im6 ~~    SAT_1   0.966  0.022   0.022    0.061    0.061
## 498       RI =~      Im4   0.963 -0.045  -0.027   -0.020   -0.020
## 499     Im10 ~~     Im17   0.961 -0.012  -0.012   -0.113   -0.113
## 500    BRAND =~   COM_A4   0.952 -0.042  -0.051   -0.029   -0.029
## 501    ATMOS =~      Im3   0.949  0.025   0.031    0.023    0.023
## 502   COM_A1 ~~   C_REP1   0.940 -0.020  -0.020   -0.052   -0.052
## 503     Im18 ~~    SAT_1   0.938 -0.022  -0.022   -0.060   -0.060
## 504   FRENCH =~      Im5   0.935  0.044   0.043    0.032    0.032
## 505     Im20 ~~    SAT_3   0.923  0.037   0.037    0.054    0.054
## 506      Im7 ~~    C_CR4   0.917  0.042   0.042    0.102    0.102
## 507      COI =~      Im5   0.909  0.024   0.041    0.031    0.031
## 508      Im1 ~~   COM_A2   0.904  0.026   0.026    0.107    0.107
## 509      SAT =~     Im16   0.904 -0.073  -0.064   -0.053   -0.053
## 510     Im13 ~~   COM_A4   0.897  0.034   0.034    0.060    0.060
## 511      SAT =~     Im21   0.881  0.051   0.045    0.033    0.033
## 512     Im22 ~~    C_CR1   0.880 -0.049  -0.049   -0.067   -0.067
## 513   FRENCH =~     Im13   0.879 -0.040  -0.039   -0.032   -0.032
## 514       RI =~      Im7   0.874 -0.069  -0.041   -0.034   -0.034
## 515      COI =~      Im4   0.873 -0.014  -0.025   -0.018   -0.018
## 516     Im18 ~~      Im7   0.866 -0.023  -0.023   -0.094   -0.094
## 517      COI =~   COM_A1   0.866 -0.028  -0.047   -0.033   -0.033
## 518     Im20 ~~     Im18   0.861  0.030   0.030    0.052    0.052
## 519     PROF =~   COM_A1   0.858  0.049   0.046    0.032    0.032
## 520     Im14 ~~     Im21   0.856  0.015   0.015    0.068    0.068
## 521   COM_A2 ~~    C_CR3   0.843 -0.057  -0.057   -0.055   -0.055
## 522    SAT_3 ~~   C_REP3   0.841  0.015   0.015    0.048    0.048
## 523     Im20 ~~   COM_A3   0.836 -0.040  -0.040   -0.053   -0.053
## 524     DECO =~    SAT_2   0.835  0.027   0.034    0.033    0.033
## 525     Im18 ~~   COM_A2   0.834  0.032   0.032    0.051    0.051
## 526      Im4 ~~     Im22   0.833 -0.020  -0.020   -0.081   -0.081
## 527     PROF =~      Im6   0.833  0.049   0.045    0.037    0.037
## 528    BRAND =~     Im10   0.829 -0.017  -0.021   -0.023   -0.023
## 529    BRAND =~     Im14   0.829  0.017   0.020    0.024    0.024
## 530    AFCOM =~     Im14   0.828  0.016   0.019    0.022    0.022
## 531     Im19 ~~   COM_A2   0.825 -0.031  -0.031   -0.057   -0.057
## 532     Im12 ~~      Im2   0.821 -0.018  -0.018   -0.056   -0.056
## 533     Im13 ~~      Im6   0.818  0.023   0.023    0.053    0.053
## 534     PROF =~     Im22   0.815  0.058   0.054    0.035    0.035
## 535     Im19 ~~    SAT_1   0.808 -0.021  -0.021   -0.068   -0.068
## 536      Im4 ~~      Im7   0.801 -0.015  -0.015   -0.129   -0.129
## 537    SAT_3 ~~    C_CR1   0.797  0.047   0.047    0.054    0.054
## 538     Im11 ~~     Im18   0.795  0.029   0.029    0.045    0.045
## 539       RI =~     Im13   0.794  0.063   0.037    0.031    0.031
## 540     Im13 ~~     Im19   0.794  0.023   0.023    0.062    0.062
## 541    BRAND =~    SAT_1   0.791 -0.027  -0.032   -0.032   -0.032
## 542      Im3 ~~    SAT_1   0.785  0.014   0.014    0.062    0.062
## 543     Im12 ~~    C_CR4   0.776  0.038   0.038    0.058    0.058
## 544     Im17 ~~      Im7   0.776 -0.019  -0.019   -0.180   -0.180
## 545      Im9  ~   CHOICE   0.774  0.035   0.046    0.034    0.034
## 546     PROF =~     Im17   0.773  0.078   0.072    0.058    0.058
## 547     PROF =~     Im18   0.772 -0.078  -0.072   -0.051   -0.051
## 548     Im17 ~~   C_REP3   0.771  0.010   0.010    0.087    0.087
## 549   CHOICE =~    C_CR1   0.761 -0.041  -0.053   -0.027   -0.027
## 550     Im22 ~~     Im17   0.759  0.023   0.023    0.105    0.105
## 551     Im11 ~~    C_CR4   0.750  0.049   0.049    0.046    0.046
## 552      Im4 ~~      Im5   0.748  0.030   0.030    0.103    0.103
## 553      Im4 ~~     Im16   0.746  0.018   0.018    0.068    0.068
## 554   COM_A4 ~~    SAT_2   0.743  0.028   0.028    0.052    0.052
## 555     Im10 ~~   COM_A3   0.739 -0.017  -0.017   -0.054   -0.054
## 556    BRAND =~     Im11   0.738 -0.039  -0.047   -0.041   -0.041
## 557      Im5 ~~     Im22   0.738  0.031   0.031    0.051    0.051
## 558    BRAND =~      Im1   0.736 -0.037  -0.045   -0.034   -0.034
## 559     Im17 ~~   C_REP2   0.735  0.009   0.009    0.129    0.129
## 560      SAT =~     Im10   0.732 -0.022  -0.020   -0.022   -0.022
## 561    SAT_3 ~~   C_REP2   0.731 -0.012  -0.012   -0.066   -0.066
## 562     Im19 ~~     Im17   0.731  0.020   0.020    0.106    0.106
## 563     Im14 ~~    C_CR4   0.726  0.021   0.021    0.066    0.066
## 564       RI =~      Im6   0.725  0.054   0.032    0.027    0.027
## 565     FOOD  ~      Im9   0.721  0.018   0.022    0.029    0.022
## 566      SAT  ~    BRAND   0.719  0.036   0.049    0.049    0.049
## 567    AFCOM =~    SAT_3   0.719  0.033   0.037    0.033    0.033
## 568      SAT =~    C_CR3   0.712 -0.066  -0.058   -0.028   -0.028
## 569 PRODQUAL =~     Im19   0.704  0.072   0.051    0.045    0.045
## 570    ATMOS  ~      Im9   0.704  0.029   0.023    0.032    0.023
## 571     Im22 ~~      Im6   0.701  0.026   0.026    0.052    0.052
## 572    ATMOS =~      Im2   0.700 -0.028  -0.035   -0.028   -0.028
## 573     Im10 ~~    C_CR4   0.698 -0.021  -0.021   -0.053   -0.053
## 574     Im21 ~~   C_REP1   0.692 -0.016  -0.016   -0.044   -0.044
## 575     Im22 ~~   COM_A3   0.689  0.035   0.035    0.053    0.053
## 576    SAT_1 ~~    C_CR3   0.683 -0.034  -0.034   -0.056   -0.056
## 577     Im13 ~~      Im7   0.677 -0.020  -0.020   -0.096   -0.096
## 578      Im5 ~~   C_REP2   0.677 -0.011  -0.011   -0.060   -0.060
## 579     Im11 ~~   COM_A1   0.673 -0.033  -0.033   -0.042   -0.042
## 580     Im11 ~~   COM_A2   0.671  0.034   0.034    0.043    0.043
## 581      Im5 ~~     Im11   0.670  0.031   0.031    0.039    0.039
## 582     Im10 ~~    C_CR3   0.668 -0.021  -0.021   -0.054   -0.054
## 583     PROF =~     Im11   0.667  0.052   0.048    0.042    0.042
## 584     Im22 ~~   COM_A4   0.663  0.035   0.035    0.054    0.054
## 585   COM_A3 ~~    SAT_3   0.663 -0.035  -0.035   -0.044   -0.044
## 586      COI =~    SAT_3   0.661 -0.021  -0.036   -0.032   -0.032
## 587     Im10 ~~   COM_A4   0.653 -0.016  -0.016   -0.052   -0.052
## 588     Im20 ~~      Im7   0.651  0.024   0.024    0.087    0.087
## 589      Im7 ~~   COM_A3   0.649  0.027   0.027    0.084    0.084
## 590      COI =~   C_REP3   0.642 -0.009  -0.015   -0.027   -0.027
## 591     Im17 ~~   COM_A3   0.642  0.024   0.024    0.082    0.082
## 592     Im22 ~~      Im7   0.641  0.024   0.024    0.098    0.098
## 593      COI =~   COM_A3   0.638 -0.026  -0.044   -0.027   -0.027
## 594     Im10 ~~   COM_A1   0.636 -0.014  -0.014   -0.049   -0.049
## 595      SAT  ~ PRODQUAL   0.635  0.057   0.046    0.046    0.046
## 596      Im6 ~~    C_CR4   0.631 -0.037  -0.037   -0.044   -0.044
## 597   C_REP2 ~~    C_CR3   0.629  0.017   0.017    0.066    0.066
## 598     Im16 ~~   COM_A3   0.629  0.033   0.033    0.045    0.045
## 599      Im4 ~~     Im12   0.620  0.013   0.013    0.069    0.069
## 600     Im14 ~~     Im18   0.616 -0.011  -0.011   -0.058   -0.058
## 601    BRAND =~    SAT_3   0.604 -0.030  -0.037   -0.033   -0.033
## 602      Im5 ~~    C_CR4   0.597  0.042   0.042    0.041    0.041
## 603 PRODQUAL =~     Im22   0.595 -0.060  -0.043   -0.028   -0.028
## 604     Im14 ~~    C_CR3   0.587  0.019   0.019    0.061    0.061
## 605    ATMOS =~     Im16   0.586 -0.035  -0.044   -0.036   -0.036
## 606     Im21 ~~   COM_A4   0.583 -0.034  -0.034   -0.043   -0.043
## 607      Im4 ~~   C_REP3   0.580 -0.007  -0.007   -0.056   -0.056
## 608     Im16 ~~   COM_A4   0.580 -0.032  -0.032   -0.044   -0.044
## 609     Im19 ~~     Im18   0.577 -0.020  -0.020   -0.047   -0.047
## 610    BRAND =~      Im2   0.565  0.029   0.035    0.027    0.027
## 611     Im17 ~~    SAT_2   0.565  0.015   0.015    0.081    0.081
## 612    AFCOM  ~    BRAND   0.546  0.040   0.042    0.042    0.042
## 613       RI =~     Im18   0.539 -0.051  -0.030   -0.022   -0.022
## 614   COM_A4 ~~   C_REP2   0.534 -0.012  -0.012   -0.060   -0.060
## 615     Im20 ~~      Im2   0.522 -0.018  -0.018   -0.041   -0.041
## 616   FRENCH =~    SAT_2   0.520  0.025   0.024    0.024    0.024
## 617     Im19 ~~   COM_A3   0.500 -0.025  -0.025   -0.044   -0.044
## 618     Im21 ~~    SAT_2   0.500 -0.020  -0.020   -0.041   -0.041
## 619     Im16 ~~    SAT_3   0.497  0.026   0.026    0.039    0.039
## 620    BRAND  ~      COI   0.495 -0.056  -0.079   -0.079   -0.079
## 621     Im10 ~~    SAT_3   0.495  0.012   0.012    0.043    0.043
## 622      Im6 ~~   COM_A3   0.489 -0.025  -0.025   -0.038   -0.038
## 623   CHOICE =~      Im3   0.486 -0.016  -0.021   -0.016   -0.016
## 624   C_REP3 ~~    C_CR1   0.486  0.015   0.015    0.041    0.041
## 625     Im13 ~~   COM_A3   0.484 -0.025  -0.025   -0.043   -0.043
## 626   CHOICE =~     Im11   0.479 -0.027  -0.035   -0.030   -0.030
## 627     DECO  ~       RI   0.474 -0.168  -0.080   -0.080   -0.080
## 628 PRODQUAL =~   COM_A1   0.474  0.046   0.033    0.023    0.023
## 629      Im3 ~~     Im19   0.473  0.013   0.013    0.047    0.047
## 630     Im17 ~~      Im6   0.472  0.015   0.015    0.068    0.068
## 631   FRENCH  ~       RI   0.467  0.167   0.101    0.101    0.101
## 632     Im10 ~~     Im18   0.463  0.010   0.010    0.041    0.041
## 633      COI =~     Im19   0.461  0.019   0.031    0.028    0.028
## 634      Im1 ~~    C_CR1   0.459 -0.024  -0.024   -0.084   -0.084
## 635     Im13 ~~   COM_A1   0.456  0.022   0.022    0.041    0.041
## 636      Im6 ~~    SAT_3   0.452 -0.021  -0.021   -0.035   -0.035
## 637    SAT_1 ~~   C_REP1   0.452  0.009   0.009    0.042    0.042
## 638     FOOD =~     Im22   0.446  0.039   0.032    0.021    0.021
## 639     Im20 ~~   C_REP3   0.443 -0.011  -0.011   -0.037   -0.037
## 640     Im21 ~~     Im17   0.443  0.018   0.018    0.067    0.067
## 641      Im3 ~~     Im20   0.441 -0.015  -0.015   -0.042   -0.042
## 642   COM_A2 ~~   C_REP2   0.440 -0.010  -0.010   -0.054   -0.054
## 643    ATMOS =~     Im10   0.426 -0.012  -0.015   -0.017   -0.017
## 644    ATMOS =~     Im14   0.425  0.012   0.015    0.017    0.017
## 645     Im11 ~~    SAT_2   0.424 -0.019  -0.019   -0.036   -0.036
## 646     FOOD =~      Im4   0.422 -0.023  -0.019   -0.014   -0.014
## 647     DECO  ~     Im15   0.422  0.023   0.018    0.022    0.018
## 648   COM_A1 ~~    C_CR4   0.422 -0.038  -0.038   -0.036   -0.036
## 649    AFCOM =~     Im10   0.418 -0.012  -0.014   -0.015   -0.015
## 650       RI =~     Im20   0.417  0.055   0.032    0.022    0.022
## 651     Im19 ~~   C_REP3   0.417  0.008   0.008    0.039    0.039
## 652      COI =~     Im22   0.416 -0.018  -0.031   -0.020   -0.020
## 653     Im10 ~~      Im2   0.412 -0.007  -0.007   -0.039   -0.039
## 654     Im22 ~~   COM_A2   0.409  0.026   0.026    0.042    0.042
## 655   COM_A2 ~~    C_CR4   0.406 -0.039  -0.039   -0.037   -0.037
## 656     FOOD  ~     Im15   0.406 -0.015  -0.018   -0.022   -0.018
## 657 PRODQUAL =~     Im20   0.404  0.048   0.034    0.023    0.023
## 658     Im12 ~~   C_REP2   0.404  0.007   0.007    0.058    0.058
## 659     Im17 ~~    SAT_3   0.403 -0.017  -0.017   -0.063   -0.063
## 660       RI =~      Im2   0.400  0.034   0.020    0.016    0.016
## 661     FOOD =~   COM_A2   0.396 -0.037  -0.030   -0.019   -0.019
## 662     FOOD =~   COM_A1   0.394 -0.035  -0.029   -0.020   -0.020
## 663     Im21 ~~   COM_A1   0.389  0.025   0.025    0.033    0.033
## 664    ATMOS =~      Im1   0.389  0.024   0.030    0.022    0.022
## 665     FOOD =~     Im19   0.388 -0.042  -0.035   -0.031   -0.031
## 666     Im17 ~~    C_CR1   0.386 -0.023  -0.023   -0.072   -0.072
## 667     DECO =~     Im11   0.386  0.025   0.031    0.027    0.027
## 668    ATMOS  ~      Im8   0.383  0.028   0.022    0.023    0.022
## 669      Im5 ~~     Im21   0.382 -0.023  -0.023   -0.031   -0.031
## 670     Im10 ~~     Im22   0.380 -0.010  -0.010   -0.044   -0.044
## 671      Im6 ~~   COM_A2   0.378  0.021   0.021    0.034    0.034
## 672      SAT =~      Im6   0.376  0.027   0.024    0.020    0.020
## 673   CHOICE  ~      Im8   0.374 -0.026  -0.020   -0.021   -0.020
## 674      COI =~      Im3   0.367  0.009   0.016    0.012    0.012
## 675      COI =~     Im21   0.362  0.017   0.028    0.020    0.020
## 676   CHOICE =~    SAT_2   0.362 -0.019  -0.025   -0.025   -0.025
## 677      Im2 ~~   COM_A1   0.362 -0.016  -0.016   -0.032   -0.032
## 678   COM_A2 ~~    SAT_1   0.358 -0.018  -0.018   -0.039   -0.039
## 679      Im2 ~~   COM_A4   0.352  0.017   0.017    0.033    0.033
## 680      Im5 ~~    C_CR3   0.349 -0.033  -0.033   -0.032   -0.032
## 681      Im5 ~~   COM_A4   0.345 -0.025  -0.025   -0.031   -0.031
## 682     Im14 ~~   C_REP1   0.333  0.005   0.005    0.042    0.042
## 683     Im10 ~~     Im19   0.332 -0.008  -0.008   -0.041   -0.041
## 684      Im3 ~~      Im7   0.330 -0.010  -0.010   -0.065   -0.065
## 685     Im14 ~~    SAT_1   0.321 -0.007  -0.007   -0.049   -0.049
## 686     Im16 ~~   COM_A1   0.318 -0.021  -0.021   -0.031   -0.031
## 687     DECO =~    SAT_3   0.318 -0.021  -0.026   -0.023   -0.023
## 688      Im2 ~~      Im7   0.317  0.011   0.011    0.057    0.057
## 689     Im19 ~~      Im7   0.310  0.014   0.014    0.069    0.069
## 690      Im7 ~~    C_CR1   0.309 -0.023  -0.023   -0.065   -0.065
## 691      Im3 ~~    SAT_2   0.308 -0.009  -0.009   -0.036   -0.036
## 692     Im22 ~~     Im16   0.307  0.020   0.020    0.036    0.036
## 693    BRAND =~   C_REP2   0.306  0.009   0.011    0.017    0.017
## 694      Im2 ~~     Im19   0.306 -0.012  -0.012   -0.034   -0.034
## 695   CHOICE =~    C_CR3   0.300 -0.027  -0.035   -0.017   -0.017
## 696      Im5 ~~   COM_A1   0.296 -0.021  -0.021   -0.028   -0.028
## 697 PRODQUAL =~     Im10   0.294 -0.021  -0.015   -0.017   -0.017
## 698 PRODQUAL =~     Im14   0.294  0.021   0.015    0.017    0.017
## 699     Im21 ~~     Im16   0.292 -0.020  -0.020   -0.030   -0.030
## 700     DECO =~      Im1   0.291 -0.019  -0.024   -0.018   -0.018
## 701     DECO =~      Im2   0.291  0.017   0.021    0.016    0.016
## 702    AFCOM =~      Im4   0.290 -0.013  -0.014   -0.011   -0.011
## 703    AFCOM =~     Im13   0.286 -0.019  -0.021   -0.018   -0.018
## 704      Im7 ~~    SAT_2   0.286 -0.012  -0.012   -0.058   -0.058
## 705    AFCOM =~    C_CR3   0.285 -0.034  -0.039   -0.019   -0.019
## 706       RI =~      Im1   0.283 -0.032  -0.019   -0.014   -0.014
## 707   CHOICE =~      Im4   0.281 -0.012  -0.016   -0.012   -0.012
## 708     Im14 ~~   C_REP2   0.280 -0.003  -0.003   -0.057   -0.057
## 709      Im5 ~~     Im17   0.279  0.014   0.014    0.050    0.050
## 710   COM_A3 ~~    C_CR3   0.278  0.034   0.034    0.031    0.031
## 711     Im20 ~~    C_CR1   0.277  0.028   0.028    0.034    0.034
## 712       RI =~    C_CR1   0.276 -0.056  -0.033   -0.017   -0.017
## 713    SAT_2 ~~    C_CR1   0.275 -0.021  -0.021   -0.034   -0.034
## 714     FOOD ~~    AFCOM   0.273  0.016   0.020    0.020    0.020
## 715     FOOD  ~    AFCOM   0.273  0.017   0.024    0.024    0.024
## 716      Im1 ~~    SAT_3   0.272  0.013   0.013    0.056    0.056
## 717      Im6 ~~   C_REP3   0.269 -0.007  -0.007   -0.027   -0.027
## 718     PROF =~      Im3   0.266  0.025   0.023    0.017    0.017
## 719    SAT_2 ~~    C_CR4   0.258  0.021   0.021    0.031    0.031
## 720     Im16 ~~    C_CR3   0.258 -0.028  -0.028   -0.030   -0.030
## 721     Im14 ~~     Im11   0.257  0.008   0.008    0.035    0.035
## 722   COM_A2 ~~   C_REP3   0.256 -0.009  -0.009   -0.028   -0.028
## 723     Im17 ~~   COM_A2   0.252 -0.014  -0.014   -0.052   -0.052
## 724     Im11 ~~   COM_A4   0.250  0.022   0.022    0.027    0.027
## 725   CHOICE =~   COM_A4   0.248 -0.019  -0.025   -0.014   -0.014
## 726     Im10 ~~    SAT_1   0.245  0.006   0.006    0.035    0.035
## 727     DECO =~    SAT_1   0.245 -0.015  -0.019   -0.018   -0.018
## 728     Im10 ~~     Im21   0.243 -0.008  -0.008   -0.030   -0.030
## 729     Im21 ~~      Im2   0.242  0.013   0.013    0.026    0.026
## 730     Im21 ~~   COM_A2   0.242  0.020   0.020    0.027    0.027
## 731   CHOICE =~     Im17   0.237  0.020   0.026    0.021    0.021
## 732   CHOICE =~     Im18   0.237 -0.020  -0.026   -0.019   -0.019
## 733      Im8  ~   CHOICE   0.237 -0.015  -0.020   -0.019   -0.019
## 734       RI =~   COM_A4   0.233  0.049   0.029    0.016    0.016
## 735     Im20 ~~   C_REP1   0.233 -0.009  -0.009   -0.027   -0.027
## 736     Im16 ~~   C_REP1   0.232  0.009   0.009    0.027    0.027
## 737       RI =~   COM_A3   0.231  0.047   0.028    0.017    0.017
## 738     Im21 ~~      Im1   0.231  0.012   0.012    0.052    0.052
## 739     FOOD =~     Im21   0.228  0.027   0.022    0.016    0.016
## 740      Im6 ~~    C_CR1   0.227  0.021   0.021    0.028    0.028
## 741   FRENCH =~      Im3   0.227 -0.014  -0.013   -0.010   -0.010
## 742     DECO =~   C_REP2   0.219 -0.007  -0.009   -0.014   -0.014
## 743 PRODQUAL =~      Im3   0.218  0.021   0.015    0.011    0.011
## 744       RI =~     Im19   0.217  0.039   0.023    0.020    0.020
## 745    ATMOS  ~       RI   0.217 -0.153  -0.072   -0.072   -0.072
## 746      Im1 ~~      Im6   0.216 -0.010  -0.010   -0.050   -0.050
## 747     Im12 ~~   C_REP3   0.215 -0.006  -0.006   -0.028   -0.028
## 748      Im4 ~~    SAT_1   0.215 -0.007  -0.007   -0.041   -0.041
## 749     Im17 ~~    SAT_1   0.211  0.009   0.009    0.054    0.054
## 750     Im21 ~~    C_CR1   0.207  0.024   0.024    0.028    0.028
## 751      COI =~    SAT_1   0.203 -0.009  -0.016   -0.015   -0.015
## 752    BRAND =~     Im19   0.202  0.024   0.028    0.025    0.025
## 753    AFCOM  ~      Im9   0.201  0.015   0.013    0.018    0.013
## 754      Im4 ~~    SAT_2   0.200 -0.007  -0.007   -0.036   -0.036
## 755 PRODQUAL =~   COM_A4   0.197 -0.034  -0.024   -0.014   -0.014
## 756      Im1 ~~     Im16   0.196 -0.011  -0.011   -0.051   -0.051
## 757     Im16 ~~    SAT_2   0.196  0.012   0.012    0.027    0.027
## 758      Im3 ~~   COM_A1   0.195 -0.010  -0.010   -0.026   -0.026
## 759     Im15  ~   FRENCH   0.191  0.022   0.021    0.018    0.018
## 760     Im14 ~~      Im1   0.186 -0.005  -0.005   -0.065   -0.065
## 761      Im2 ~~    C_CR4   0.185 -0.016  -0.016   -0.024   -0.024
## 762     Im14 ~~     Im22   0.183  0.007   0.007    0.037    0.037
## 763   CHOICE =~    SAT_1   0.182  0.014   0.018    0.018    0.018
## 764     FOOD =~   C_REP3   0.182 -0.010  -0.008   -0.014   -0.014
## 765     Im18 ~~   C_REP2   0.179 -0.005  -0.005   -0.033   -0.033
## 766     Im13 ~~    SAT_1   0.177 -0.009  -0.009   -0.030   -0.030
## 767     Im21 ~~      Im7   0.175 -0.012  -0.012   -0.042   -0.042
## 768     Im18 ~~    C_CR1   0.175  0.019   0.019    0.025    0.025
## 769     Im19 ~~   COM_A4   0.173 -0.015  -0.015   -0.027   -0.027
## 770      Im5 ~~    SAT_3   0.172 -0.015  -0.015   -0.021   -0.021
## 771     Im16 ~~     Im18   0.170 -0.013  -0.013   -0.023   -0.023
## 772     Im17 ~~    C_CR4   0.170  0.016   0.016    0.044    0.044
## 773   CHOICE =~      Im6   0.169 -0.012  -0.015   -0.013   -0.013
## 774     Im11 ~~    C_CR1   0.169 -0.022  -0.022   -0.024   -0.024
## 775     DECO =~    C_CR3   0.167  0.021   0.026    0.013    0.013
## 776   CHOICE =~   C_REP2   0.166 -0.006  -0.008   -0.012   -0.012
## 777     Im12 ~~   COM_A1   0.162  0.012   0.012    0.025    0.025
## 778   COM_A3 ~~    C_CR1   0.161 -0.024  -0.024   -0.025   -0.025
## 779   FRENCH =~    C_CR3   0.160 -0.027  -0.026   -0.013   -0.013
## 780    SAT_3 ~~    C_CR4   0.159  0.022   0.022    0.022    0.022
## 781      Im4 ~~   COM_A2   0.155 -0.009  -0.009   -0.031   -0.031
## 782      Im3 ~~   C_REP3   0.155  0.004   0.004    0.023    0.023
## 783      Im5 ~~    SAT_1   0.153 -0.010  -0.010   -0.023   -0.023
## 784   FRENCH =~     Im18   0.151  0.016   0.016    0.011    0.011
## 785   FRENCH =~     Im17   0.151 -0.016  -0.016   -0.013   -0.013
## 786      SAT =~   C_REP3   0.149 -0.009  -0.008   -0.015   -0.015
## 787      Im4 ~~   COM_A1   0.149  0.009   0.009    0.029    0.029
## 788     Im11 ~~     Im16   0.148 -0.014  -0.014   -0.020   -0.020
## 789     Im19 ~~    C_CR3   0.145  0.018   0.018    0.025    0.025
## 790      Im7 ~~   C_REP1   0.143  0.006   0.006    0.038    0.038
## 791    AFCOM =~     Im18   0.141 -0.013  -0.015   -0.011   -0.011
## 792     FOOD =~   COM_A4   0.140 -0.023  -0.019   -0.011   -0.011
## 793      Im4 ~~   C_REP2   0.140  0.003   0.003    0.041    0.041
## 794     Im22 ~~    C_CR3   0.139  0.021   0.021    0.025    0.025
## 795      Im3 ~~    C_CR3   0.138 -0.012  -0.012   -0.024   -0.024
## 796     Im14 ~~   COM_A1   0.138  0.006   0.006    0.027    0.027
## 797      Im3 ~~   C_REP2   0.137 -0.003  -0.003   -0.032   -0.032
## 798    C_CR1 ~~    C_CR3   0.136  0.097   0.097    0.080    0.080
## 799   CHOICE =~   COM_A2   0.135 -0.013  -0.017   -0.011   -0.011
## 800     DECO  ~      Im8   0.131  0.014   0.012    0.012    0.012
## 801     DECO  ~      Im9   0.128  0.011   0.009    0.012    0.009
## 802      Im1 ~~      Im2   0.127  0.290   0.290    1.859    1.859
## 803   CHOICE  ~      SAT   0.127 -0.089  -0.060   -0.060   -0.060
## 804   CHOICE ~~      SAT   0.127 -0.041  -0.047   -0.047   -0.047
## 805     Im21 ~~     Im12   0.125  0.010   0.010    0.022    0.022
## 806     Im20 ~~     Im11   0.124  0.014   0.014    0.019    0.019
## 807     PROF =~    C_CR3   0.123 -0.026  -0.024   -0.011   -0.011
## 808      Im3 ~~    SAT_3   0.122 -0.008  -0.008   -0.020   -0.020
## 809     Im20 ~~     Im12   0.121  0.010   0.010    0.023    0.023
## 810     Im17 ~~    C_CR3   0.120  0.014   0.014    0.038    0.038
## 811   C_REP2 ~~    C_CR1   0.119  0.007   0.007    0.030    0.030
## 812   FRENCH =~     Im21   0.118 -0.017  -0.016   -0.012   -0.012
## 813      COI =~   COM_A4   0.117  0.012   0.020    0.011    0.011
## 814    BRAND  ~      SAT   0.116  0.024   0.018    0.018    0.018
## 815    BRAND ~~      SAT   0.116  0.011   0.014    0.014    0.014
## 816     PROF =~     Im21   0.115  0.021   0.019    0.014    0.014
## 817      Im3 ~~    C_CR4   0.115 -0.011  -0.011   -0.021   -0.021
## 818    BRAND  ~    AFCOM   0.113 -0.016  -0.015   -0.015   -0.015
## 819    BRAND ~~    AFCOM   0.113 -0.014  -0.012   -0.012   -0.012
## 820      Im4 ~~     Im14   0.113 -0.003  -0.003   -0.035   -0.035
## 821     Im14 ~~    SAT_3   0.112 -0.005  -0.005   -0.024   -0.024
## 822    ATMOS =~    SAT_1   0.110  0.009   0.012    0.012    0.012
## 823       RI =~    C_CR4   0.102  0.035   0.021    0.010    0.010
## 824     DECO =~   COM_A1   0.102 -0.012  -0.015   -0.010   -0.010
## 825      Im4 ~~    C_CR4   0.100  0.010   0.010    0.025    0.025
## 826    ATMOS =~     Im19   0.100 -0.014  -0.018   -0.016   -0.016
## 827     PROF  ~      Im9   0.100 -0.007  -0.008   -0.011   -0.008
## 828    AFCOM =~     Im19   0.098 -0.011  -0.012   -0.011   -0.011
## 829     Im16 ~~   C_REP2   0.095  0.004   0.004    0.025    0.025
## 830      Im1 ~~    C_CR3   0.093 -0.011  -0.011   -0.036   -0.036
## 831     DECO =~     Im16   0.092 -0.018  -0.023   -0.019   -0.019
## 832     DECO =~     Im19   0.092  0.019   0.023    0.021    0.021
## 833   CHOICE  ~      Im9   0.091 -0.010  -0.008   -0.011   -0.008
## 834      Im6 ~~    SAT_2   0.090 -0.007  -0.007   -0.017   -0.017
## 835     DECO =~   COM_A4   0.088  0.012   0.015    0.009    0.009
## 836    SAT_2 ~~   C_REP3   0.083  0.003   0.003    0.016    0.016
## 837     PROF =~    SAT_3   0.083 -0.020  -0.018   -0.016   -0.016
## 838     Im18 ~~    C_CR3   0.081 -0.014  -0.014   -0.016   -0.016
## 839   FRENCH =~   C_REP3   0.081 -0.005  -0.005   -0.009   -0.009
## 840      Im2 ~~      Im6   0.081 -0.006  -0.006   -0.015   -0.015
## 841     Im20 ~~    C_CR3   0.081 -0.016  -0.016   -0.017   -0.017
## 842      Im5 ~~     Im18   0.081  0.009   0.009    0.014    0.014
## 843    ATMOS =~    SAT_3   0.079 -0.010  -0.013   -0.012   -0.012
## 844     Im18 ~~    C_CR4   0.077 -0.013  -0.013   -0.015   -0.015
## 845      Im1 ~~    C_CR4   0.073 -0.010  -0.010   -0.031   -0.031
## 846     Im18 ~~    SAT_2   0.072  0.006   0.006    0.015    0.015
## 847      Im5 ~~     Im12   0.071  0.008   0.008    0.016    0.016
## 848      Im8  ~    BRAND   0.070 -0.009  -0.011   -0.010   -0.010
## 849      COI =~     Im12   0.069  0.006   0.010    0.009    0.009
## 850     Im11 ~~     Im19   0.068 -0.008  -0.008   -0.015   -0.015
## 851    SAT_1 ~~   C_REP3   0.067  0.003   0.003    0.016    0.016
## 852      Im2 ~~   COM_A2   0.067 -0.007  -0.007   -0.014   -0.014
## 853      Im6 ~~   C_REP1   0.063 -0.004  -0.004   -0.013   -0.013
## 854      COI =~     Im20   0.062  0.007   0.012    0.008    0.008
## 855     Im12 ~~     Im18   0.062 -0.006  -0.006   -0.016   -0.016
## 856     Im18 ~~   COM_A4   0.061 -0.009  -0.009   -0.014   -0.014
## 857     FOOD =~     Im17   0.061  0.013   0.010    0.008    0.008
## 858     FOOD =~     Im18   0.061 -0.012  -0.010   -0.007   -0.007
## 859     DECO ~~    AFCOM   0.061 -0.011  -0.009   -0.009   -0.009
## 860     DECO  ~    AFCOM   0.061 -0.012  -0.011   -0.011   -0.011
## 861   FRENCH =~     Im10   0.060 -0.010  -0.010   -0.011   -0.011
## 862   FRENCH =~     Im14   0.060  0.010   0.010    0.011    0.011
## 863     Im10 ~~   C_REP2   0.059 -0.002  -0.002   -0.021   -0.021
## 864      Im4 ~~     Im20   0.058 -0.005  -0.005   -0.019   -0.019
## 865       RI =~    C_CR3   0.056  0.027   0.016    0.008    0.008
## 866      Im2 ~~    C_CR3   0.056  0.009   0.009    0.014    0.014
## 867      COI =~     Im17   0.055 -0.005  -0.009   -0.007   -0.007
## 868      Im4 ~~     Im21   0.055  0.005   0.005    0.018    0.018
## 869     FOOD  ~      COI   0.052 -0.013  -0.027   -0.027   -0.027
## 870     Im21 ~~     Im13   0.051 -0.007  -0.007   -0.014   -0.014
## 871      COI =~      Im6   0.051 -0.005  -0.008   -0.007   -0.007
## 872       RI =~     Im17   0.050  0.015   0.009    0.007    0.007
## 873     Im21 ~~   COM_A3   0.050 -0.010  -0.010   -0.012   -0.012
## 874   COM_A2 ~~   C_REP1   0.049  0.005   0.005    0.012    0.012
## 875   CHOICE =~    SAT_3   0.049  0.009   0.011    0.010    0.010
## 876    BRAND =~    C_CR3   0.048 -0.012  -0.014   -0.007   -0.007
## 877     Im19 ~~      Im6   0.044 -0.005  -0.005   -0.013   -0.013
## 878      Im4 ~~    SAT_3   0.043  0.004   0.004    0.015    0.015
## 879   C_REP1 ~~    C_CR1   0.043 -0.006  -0.006   -0.012   -0.012
## 880    AFCOM =~      Im3   0.042 -0.005  -0.006   -0.004   -0.004
## 881      Im3 ~~     Im13   0.042  0.004   0.004    0.014    0.014
## 882 PRODQUAL =~     Im21   0.042  0.015   0.011    0.008    0.008
## 883      Im1 ~~     Im19   0.041 -0.004  -0.004   -0.027   -0.027
## 884     FOOD =~    C_CR3   0.041 -0.016  -0.013   -0.006   -0.006
## 885    C_CR1 ~~    C_CR4   0.039 -0.046  -0.046   -0.038   -0.038
## 886    SAT_3 ~~   C_REP1   0.037 -0.004  -0.004   -0.010   -0.010
## 887     Im11 ~~    C_CR3   0.036  0.011   0.011    0.010    0.010
## 888     Im11 ~~    SAT_3   0.035 -0.007  -0.007   -0.009   -0.009
## 889     DECO =~     Im10   0.035 -0.004  -0.005   -0.005   -0.005
## 890     DECO =~     Im14   0.035  0.004   0.005    0.005    0.005
## 891     Im10 ~~      Im1   0.034 -0.002  -0.002   -0.023   -0.023
## 892 PRODQUAL =~    SAT_3   0.032  0.012   0.009    0.008    0.008
## 893 PRODQUAL  ~      SAT   0.031 -0.008  -0.010   -0.010   -0.010
## 894 PRODQUAL ~~      SAT   0.031 -0.004  -0.008   -0.008   -0.008
## 895       RI =~    SAT_3   0.031 -0.014  -0.008   -0.008   -0.008
## 896      SAT =~      Im7   0.029 -0.008  -0.007   -0.006   -0.006
## 897      Im3 ~~     Im16   0.029 -0.004  -0.004   -0.011   -0.011
## 898   FRENCH =~     Im19   0.028  0.009   0.008    0.007    0.007
## 899     DECO =~     Im21   0.028 -0.007  -0.008   -0.006   -0.006
## 900      COI =~     Im14   0.027 -0.002  -0.003   -0.004   -0.004
## 901   FRENCH =~      Im4   0.027  0.005   0.005    0.003    0.003
## 902 PRODQUAL  ~      Im8   0.027  0.004   0.006    0.006    0.006
## 903     FOOD =~    SAT_1   0.027 -0.007  -0.006   -0.005   -0.005
## 904     FOOD =~      Im3   0.026 -0.006  -0.005   -0.004   -0.004
## 905      Im3 ~~     Im21   0.026 -0.004  -0.004   -0.009   -0.009
## 906     PROF =~   C_REP2   0.026  0.004   0.003    0.005    0.005
## 907      Im1 ~~      Im7   0.025 -0.003  -0.003   -0.034   -0.034
## 908     Im13 ~~    C_CR1   0.024 -0.007  -0.007   -0.010   -0.010
## 909    C_CR3 ~~    C_CR4   0.023 -0.036  -0.036   -0.026   -0.026
## 910      Im2 ~~    SAT_3   0.023 -0.004  -0.004   -0.008   -0.008
## 911      Im3 ~~     Im10   0.022  0.001   0.001    0.010    0.010
## 912      Im5 ~~     Im10   0.022 -0.002  -0.002   -0.009   -0.009
## 913     Im13 ~~    C_CR4   0.022  0.007   0.007    0.009    0.009
## 914      Im5 ~~   C_REP3   0.021  0.002   0.002    0.007    0.007
## 915 PRODQUAL =~   C_REP1   0.020  0.005   0.003    0.005    0.005
## 916      Im3 ~~     Im14   0.019 -0.001  -0.001   -0.011   -0.011
## 917      Im3 ~~   C_REP1   0.019  0.002   0.002    0.008    0.008
## 918      SAT =~      Im3   0.019  0.005   0.004    0.003    0.003
## 919     Im22 ~~    C_CR4   0.019  0.008   0.008    0.009    0.009
## 920    BRAND =~     Im21   0.019 -0.006  -0.007   -0.005   -0.005
## 921     Im20 ~~    C_CR4   0.018 -0.008  -0.008   -0.008   -0.008
## 922      Im5 ~~    C_CR1   0.018  0.007   0.007    0.008    0.008
## 923      Im4 ~~   C_REP1   0.018 -0.001  -0.001   -0.010   -0.010
## 924     Im14 ~~   COM_A4   0.018  0.003   0.003    0.010    0.010
## 925     Im18 ~~   COM_A3   0.018  0.005   0.005    0.007    0.007
## 926      COI =~      Im7   0.018 -0.003  -0.006   -0.005   -0.005
## 927   C_REP1 ~~    C_CR4   0.018 -0.004  -0.004   -0.007   -0.007
## 928      Im3 ~~      Im6   0.017  0.002   0.002    0.008    0.008
## 929     Im20 ~~     Im16   0.015  0.005   0.005    0.007    0.007
## 930      Im4 ~~     Im19   0.015 -0.002  -0.002   -0.011   -0.011
## 931      COI =~     Im10   0.014  0.001   0.002    0.003    0.003
## 932      Im6 ~~   COM_A4   0.014 -0.004  -0.004   -0.007   -0.007
## 933     Im10 ~~   C_REP1   0.013  0.001   0.001    0.007    0.007
## 934      Im7 ~~    SAT_1   0.011  0.002   0.002    0.013    0.013
## 935    SAT_2 ~~   C_REP2   0.010  0.001   0.001    0.008    0.008
## 936      Im1 ~~   C_REP1   0.010 -0.001  -0.001   -0.011   -0.011
## 937    AFCOM =~     Im17   0.010  0.003   0.003    0.003    0.003
## 938     Im12 ~~      Im1   0.009  0.002   0.002    0.012    0.012
## 939   COM_A3 ~~    C_CR4   0.008  0.006   0.006    0.005    0.005
## 940      Im7 ~~    C_CR3   0.008 -0.004  -0.004   -0.010   -0.010
## 941 PRODQUAL =~    C_CR3   0.007 -0.008  -0.006   -0.003   -0.003
## 942     Im13 ~~   C_REP3   0.006  0.001   0.001    0.005    0.005
## 943   COM_A4 ~~    C_CR1   0.006  0.005   0.005    0.005    0.005
## 944     Im16 ~~      Im6   0.006 -0.002  -0.002   -0.004   -0.004
## 945      Im5 ~~     Im13   0.006 -0.002  -0.002   -0.004   -0.004
## 946     Im21 ~~      Im6   0.005 -0.002  -0.002   -0.004   -0.004
## 947     DECO  ~      COI   0.005 -0.006  -0.008   -0.008   -0.008
## 948      Im4 ~~     Im13   0.004 -0.001  -0.001   -0.006   -0.006
## 949     Im19 ~~    C_CR4   0.004  0.003   0.003    0.004    0.004
## 950      Im4 ~~     Im10   0.004 -0.001  -0.001   -0.005   -0.005
## 951   FRENCH =~     Im12   0.003 -0.002  -0.002   -0.002   -0.002
## 952     PROF =~   COM_A4   0.003 -0.003  -0.003   -0.002   -0.002
## 953    BRAND =~   COM_A1   0.002  0.002   0.002    0.002    0.002
## 954      Im6 ~~    C_CR3   0.002 -0.002  -0.002   -0.003   -0.003
## 955      COI =~     Im18   0.002  0.001   0.002    0.001    0.001
## 956     Im12 ~~     Im19   0.002 -0.001  -0.001   -0.003   -0.003
## 957     Im18 ~~    SAT_3   0.001  0.001   0.001    0.002    0.002
## 958     Im19 ~~    C_CR1   0.001  0.001   0.001    0.002    0.002
## 959     PROF =~     Im10   0.001 -0.001  -0.001   -0.001   -0.001
## 960     PROF =~     Im14   0.001  0.001   0.001    0.001    0.001
## 961     Im14 ~~     Im19   0.001  0.000   0.000    0.003    0.003
## 962     Im21 ~~     Im19   0.001  0.001   0.001    0.002    0.002
## 963     FOOD =~     Im12   0.001 -0.002  -0.001   -0.001   -0.001
## 964     Im16 ~~     Im17   0.001 -0.001  -0.001   -0.003   -0.003
## 965       RI =~      Im3   0.001  0.001   0.001    0.000    0.000
## 966     Im21 ~~    SAT_1   0.000 -0.001  -0.001   -0.001   -0.001
## 967     Im16 ~~   COM_A2   0.000  0.001   0.001    0.001    0.001
## 968    ATMOS =~      Im6   0.000  0.001   0.001    0.001    0.001
## 969    ATMOS =~      Im7   0.000 -0.001  -0.001   -0.001   -0.001
## 970    SAT_1 ~~    SAT_2   0.000 -0.001  -0.001   -0.003   -0.003
## 971     Im11 ~~   C_REP3   0.000  0.000   0.000   -0.001   -0.001
## 972    AFCOM =~     Im22   0.000  0.001   0.001    0.000    0.000
## 973      Im5 ~~   COM_A3   0.000  0.000   0.000    0.001    0.001
## 974     Im21 ~~   C_REP2   0.000  0.000   0.000    0.001    0.001
## 975   CHOICE =~      Im7   0.000  0.000   0.000    0.000    0.000
## 976      COI =~   COM_A2   0.000  0.000   0.000    0.000    0.000
## 977      Im5 ~~     Im20   0.000  0.000   0.000    0.000    0.000